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1  -K'      CHARLES  SCRIBNER'S  SONS,  :T)7< 

^        '^£>i^  N  EW  YO  RKf^'  "^ 


NATURAL  SERIES. 


THE 

FIRST    LESSOI^TS 

IN   NUMBEES; 


ILLUSTEMD  TABLE.  BOOK, 

DESIGNED   FOR 

elementary  instruction.    . 

felter,ia;m.,4 

lATE  AND   POLY'ra^NIC  d^TITUW, 


%■ 


»< 


LATB  OP  THE  BROOKLYN  COLLEGIATE  AND  POLYTIBInIC  MSTITUW,   AND    AUTHOR 
OP  THE   "arithmetical   ANALYSIS,"  ETC 


UTHOR  ij  I 


\  f 


NEW  YORK: 

CHARLES   SCRIBNER'S   SONS, 
743  &  745  Broadway. 


ENTEREdfaccordin^ito  Act  of  Congress,  in  the  year  1865,  by 

S.     A.     FELTER, 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Southern  District  of 

New  York. 


Entered,  according  to  Act  of  Congress,  in  the  year  18&8,  by 
S.    A.    FE^^TER,  P 

In  the  Clerk's  Office  of  the  District  Court  nf  the  United  StateWor  the  Southern   Distiict  cf 

•         .      N*>wAnrV.  ^ 


•  New^^rk.  » 


PEEFAOE. 


In  the  preparation  of  this  little  boot;^  the  au- 
thor has  aimed  to  make  it  simply  a  convenient 
storehouse  from  which  the  Teacher  is  to  draw 
materials  for  the  instruction  of  his  pupils ;  and, 
therefore,  it  is  not  intended  to  "  exempt  the  teacher 
from  the  labor  of  explaining  orally,  setting  sums, 
&c."  It  does  not  propose  ''to  teach  the 
pupil  how  to  think, "  for  this  must  be  done  by 
a  living  teacher ;  and  no  book,  whatever  its  pre- 
tensions, can  be  more  than  an  aid.  In  the  first 
lessons,  but  little  more  should  be  done  than  to 
awaken  the  senses  to  the  perception  of  num- 
ibers  as  exhibited  in  surrounding  objects,  and 
make  the  little  pupils  acquainted  with  some  of 
the  simpler  facts.  Whoever  attempts  to  force 
upon  them  reasons,  solutions,  definitions,  and 
relations,  violates  the  fundamental  law  of  the  de- 
velopment of  the  human  mind ;  and,  although  the 
pupils  may  become  learned  in  the  book,  they  are, 
nevertheless,  on  the  broad  road  to  conceited 
ignorance. 

New  York,  May  1,  1865. 


II 


TO  THE    TEACHER 


The  teacher  will  readily  perceive  that  this  little 
book  is  emphatically  an  illustrated  table-book,  and 
not  an  elementary  Arithmetic ;  and  that  its  object 
is  to  suggest  to  the  little  pupil  something  to  do. 
While  it  is  impossible  in  a  work  so  small  to  do  more 
than  give  suggestions,  the  teacher  will  find  little  dif- 
ficulty in  supplying  the  deficiency  by  the  use  of  the 
blackboard.  Although  there  is  nothing  in  the  book 
which  the  children  ought  to  be  required  to  commit 
to  memory  as  a  set  task,  yet  each  step  should  be 
thoroughly  mastered  by  means  of  oral  and  written 
exercises  before  proceeding  to  the  next. 

To  accompany  the  series,  there  is  a  Manual  pre- 
pared expressly  for  the  use  of  the  teacher  ;  contain- 
ing model  lessons  suggestive  of  the  best  methods  of  i 
oral,  written,  individual,  and  class  instruction.     - 


FIHST  LESSONS  IN  NUMBERS. 


LESSON    I. 

Note. — Each  of  the  following  Le.-sons  is  illustrated  by  a  Model  Exer- 
cise givoii  in  detail  in  a  Teacher' b  Manual,  prepared  expressly  to  accom- 
pany this  work. 


One  stump  ;  //  1. 


Two  trees ;  ^/  2. 


Thvee  boys;  Three  kites  ;  J"/  3. 


Four  bars ;  ^ /  4.         Five  fowls ;  J /  5. 


COUNTING. 


liSSSON    II. 


Six  stones;  ^/  6. 


Seven  \QdiYQ^\  y/  7. 


Eight  boats ;  §/  8. 


i\r^W  balls;  ^/  9.       T^ti  tenpins  ;  /O/  10. 


Note  TO  THK  Teacher.— Questions  like  the  following  should  be| 
asked  on  the  foregoing  illustrations  :  How  many  chickens  stand  on  \ 
the  fence?  How  many  bouts  have  sails?  How  many  men  in  the' 
rowboat?  How  many  tenpins  stand  up?  How  many  have  fallen! 
down '{    (See  Manual  of  instruction  for  teachers.) 


COTJNTING. 

7 

i.i:ssoN 

III. 

# 

(S 

Be  Manual,  Sec.  I.,  ] 

Exercise  I.) 

Copy  and  read  the  following 

exercises : 

;  Ex.  1.      (1) 

(2) 

(3) 

W 

(«) 

(6) 

(7) 

(8) 

(9) 

(10) 

3 

s 

/ 

2 

2 

3 

2 

3 

3 

2   1 

/ 

2 

0 

3 

2 

0 

2 

2 

J" 

2 

/ 

3 

/ 

2 

^ 

4 

0 

4 

^   1 

/ 

2 

J 

2 

0 

2 

J- 

2 

J 

^  i 

2 

S 

/ 

.^ 

/ 

3 

0 

3 

3 

-g 

/ 

/ 

2 

3 

2 

3 

J 

J 

J- 

J" 

Ex.  2.     (1) 

<2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10)  \ 

k        '^ 

J 

^ 

^ 

d 

7 

^ 

3 

7 

4   \ 

1            ' 

7 

P 

7 

9 

3 

7 

/ 

7 

§ 

P             ^ 

0 

3 

/ 

7 

9 

§ 

7 

^ 

0 

7 

7 

J 

3 

3 

3 

3 

6 

^ 

3  \ 

1 

s 

s 

7 

^ 

7 

2 

7 

^ 

J" 

^  ^ 

7 

P 

3 

/ 

d 

0 

2 

3 

7 

i 

*  ^Vof^  /o/*  th&  Ten cher.— These  exercises  should  be  copied  neatly  on  the 
■  slate,  and  read  at  recitation  by  the  members  of  the  class.     Particular  atten- 
i  tion  should  be  given  to  the  formation  of  figures. 

COUNTING. 


LESSON    IV.* 

(See  Manual,  Sec.  I.,  Exorcise  I.) 


J^  =  1, 1, 1. 

S  equals  1,  1,  1,  units. 

^  ==  1, 1, 1, 1, 1. 

^or  - 

J  equals  1, 1, 1, 1, 1  units 

^  =  1, 1. 

2  equals  1,  1,  units. 

Copy  and  read  the  following  exercises : 

Ex.1.  Model.  (1)     (2)     (3)       (4)     (6)  (6) 

J"  =  1,1, 1.        ^  p  y  j^  ^  s 

.^  =  1,1, 1,1,1.  ^  7   ^   ^   7  7 

./  =  !,  1,1,1.        ^   ^    ^    7    ^  ^ 

Ex.2.      (1)       (2)        (3)        (4)       <5)        (6)        (7)      '(8)        (9)  (10) 

J   ^  p    <^  p   J,-   y^    4  p  4 

7   s    /   y   4    /   /    s    ^  / 

S4s^ss^77  ^ 

p/0S^2dd§7 

/S7^74S^s  ^ 

7§/7S^7S7  s 

*  Note  for  the  Teae?ier.— The  teacher  should  explain  the  meaning  and 
use  of  the  sign  of  equality  (=)  in  the  following  exercises. 


COUNTING. 


LESSON  V. 


Fifteen\io6k&\/J^/l?>.EighteenhriQk&\  /S',-  18. 


Ex.  J.       (1.) 


(2.)         (3.)         (4.)         (5.)        (6.)         (7.)         (8.) 


//  //  /S  /^  /S  /S  /4  /S 
/2  /^  //  /S'  /^  /^  //  // 
/S    /p    /d    //   SO    /S    /d    /<$ 

/^  20  yp  yj  /S'  //  /^  // 

/^  /4  /3  yd  /p  /^  /O  20 
Yd    /J-    /^    /S    20    /2    //    20 

Questions. — How  many  books  on  the  upper  shelf?  How  many 
are  lying  down?  How  many  bricks  in  the  pile?  How  many  bricks 
iu  the  lowest  row  ?  How  many  bricks  in  the  next  row  ?  How  many 
are  lying  on  the  ground  ?  How  many  books  are  standing  up?  How 
many  books  on  the  lower  shelf?  How  many  books  on  both  shelves? 
If  all  the  books  were  removed  from  the  lower  shelf,  how  many 
would  remain  on  the  upper  shelf?  If  I  should  take  away  three 
books  from  the  upper  shelf,  how  many  would  remain  ?  How  many 
would  remain  on  both  ?  etc. 


LESSON   VI. 

One  boy  and  1  boy  are  how  many  boys? 
Two  houses  and  1  house  are  how  many  ? 

3  cows  and  1  cow  are  how  many? 

4  sheep  and  1  sheep  are  how  many  ? 

5  trees  and  1  tree  are  how  many  ? 

6  fishes  and  1  fish  are  how  many  ? 

7  stones  and  1  stone  are  how  many  ? 

8  posts  and  1  ])ost  are  how  many? 

9  birds  and  1  bird  are  how  many  ? 


ADDITION.  11 


LESSON    VII.* 

(See  Manual,  Sec.  I.,  Exercise  II.)  ; 

Copy  and  complete  tke  following  tables : 

Ex.1.        Model.  (l.r  (2)  (3.)  (4.) 

S-^/^J-  ^+/  ^+/  ^+/  ^+/ 
J-^-Z^S    /  +  ^  /+/    J+Z    2-\-/ 

7+/=^  ^+/  /+/  /+j?  j'+y 
2a-/=j  ^+/   /+/  <!^+/  ^+/ 
4+y--=^  j'+z  ^+/  ^+X^4-./,' 
s-^y^j-  ^+/  /+/  /+/  ^Fz--. 

Ex.2.  (1.)  (2.)  (3.)  '"^^(4.)  (^.)  > 
^+/  ^+/  ^+/  (^+/  /  +  ^ 
^+/    /  +  ^    ^+/    /+/    ^+/ 

(^+/     /+/    /+/     J'+Z     /  +  (^ 

/+^  ^+/  ^H-/  /f/  /  +  / 
/+/  /+/  J^+Z  /+^  /  +  / 
^+/      J'+Z     -^4-/      /  +  /      /  +  / 

*  iV^o^e  /or  ^Ae    2Tgr/c7i€/'.— Before    copying  the    following    lessons  the 
sign  of  addition  ( +  )  should  be  explained  to  the  pupils. 


One  boy  and  2  boys  are  how  many  ? 

2  girls  and  2  girls  are  how  many  ? 

3  windows  and  2  windows  are  how  many  ? 

4  boats  and  2  boats  are  how  many  ? 

5  chicks  and  2  chicks  are  how  many? 

6  ducks  and  2  ducks  are  how  many? 

7  sheep  and  2  sheep  are  liow  many  ? 

8  plates  and  2  plates  are  how  many  ? 

9  birds  and  2  birds  are  how  many  ? 


/- 

ADDITION. 

13 

m_ 

LESSON 

IX. 

j 

■b 

(See  Manual,  Sec.  I., 

Exercise  II.) 

i 

! 

^^Copy  and 

complete  the  following  tables : 

Ex.  1.        (1.) 

C2.) 

(3.) 

(4.) 

(5.) 

1 
<6.) 

5  +  2= 

=    3  +  2 

2  +  2 

4+2 

5  +  2 

4  +  2 

4+2= 

=    2  +  3 

2  +  2 

2  +  5 

2  +  5 

2  +  2 

IK      2+4= 

=    4+2 

3  +  2 

4+2 

3  +  2 

1  +  2     ! 

K      5  +  2= 

=    2  +  5 

2  +  2 

1  +  2 

2  +  3 

2  +  1     ! 

■      2  +  2= 

=    2+4 

2  +  2 

2  +  3 

1  +  2 

3  +  2 

^      3  +  2= 

=    3  +  2 

1  +  2 

1  +  2 

2  +  1 

4+2 

Ex.  2.      (1.) 

(2.) 

(3.) 

<4.) 

(5.) 

(6-) 

2  +  1 

1+4 

2  +  3 

4  +  2 

5  +  1 

7+1 

■'        1  +  2 

3  +  2 

3  +  2 

5  +  2 

4  +  1 

4+2 

1  +  3 

2  +  3 

1  +  5 

6  +  1 

2  +  4 

1  +  2 

2+2 

4+1 

5  +  2 

1  +  6 

5  +  2 

0  +  2 

4+1 

5  +  1 

2  +  5 

2  +  5 

4  +  2 

2  +  0 

3  +  2 

1  +  5 

3  +  2 

5  +  1 

2  +  5 

4  +  2 

Ex.  3.       (1.) 

(2) 

(3.) 

(4-) 

(5-) 

(6.) 

6  +  2 

8  +  2 

3  +  2 

5  +  2 

2  +  7 

4  +  2 

IHL       2  +  6 

m      7+2 

T       2  +  '^ 

7  +  2 

5  +  2 

2  +  3 

0  +  7 

2  +  2 

6  +  2 

2  +  5 

2  +  7 

0  +  2 

5  +  2 

8  +  2 

7  +  2 

2+9 

2  +  0 

7  +  2      i 

fi         4  +  2 

1  +  2 

2  +  8 

2  +  8 

1  +  0 

6  +  2      ; 

;            7  +  2 

5+2 

2  +  7 

2  +  6 

8+0 

84-2      1 

14  ADDITION. 


LESSON    X. 

One  boy  and  3  boys  are  how  many  ? 

2  bouses  and  3  bouses  are  bow  many  ? 

3  trees  and  3  trees  are  bow  many  ? 

4  girls  and  3  girls  are  bow  many  ? 

5  caps  and  3  caps  are  bow  many  ? 

6  skates  and  3  skates  are  bow  many? 

7  posts  and  3  posts  are  bow  many  ? 

8  sleds  and  3  sleds  are  bow  many  ? 

9  boods  and  3  boods  are  bow  many? 


Note.— The  teacher  should  dictate  problems  referring  to  the  ob- 
jects in  the  illustrations,  thus  :  Two  boys  have  hold  of  hands;  how 
many  would  there  be  if  another  should  join  them?  There  are  six 
trees;  if  two  were  cut  down,  how  many  would  remain  standing? 
Two  little  girls  are  skating  and  two  are  looking  on  ;  how  many  in 
all?  There  are  five  houses  ;  if  two  should  be  burned  up  how  many 
would  remain?  If  one  boy  has  two  skates,  how  many  skates  will 
two  boys  have?  There  are  eight  boys  skating,  one  of  them  has  fallen  ' 
down;  how  many  remain  standing?  One  house  and  one  house  are;  , 
how  many  ?  One  tree  and  five  trees  are  how  many  ?  Four  trees 
(;.  and  two  trees  are  how  many  ?     Two  trees  and  four  trees  are  how 

I  maoy.t;  ! 

( 1< I 


•  1                               ^ 

ADDITION. 

15 

! 

LESSON 

XI. 

i 

(See  Manual,  Sec.    I., 

Exercise  II.) 

'   Copy,  complete,  and  read  the  following 

tables : 

Ex.  1.        (1.) 

(2) 

(3.) 

(4.) 

<5.) 

(6.) 

1  +  3 

3  +  1 

4  +  3 

1  +  5 

3+4 

4+3     ' 

3  +  1 

3  +  4 

3  +  2 

1  +  3 

2  +  4 

3  +  2     I 

3  +  4 

1  +  4 

2  +  1 

1  +  6 

4+3 

2+1 

6  +  1 

3  +  1 

1  +  3 

2  +  4 

4  +  2 

3+5 

5  +  2 

5  +  2 

4+3 

2  +  5 

5  +  2 

5  +  2 

4+3 

2  +  5 

5  +  1 

3  +  2 

5  +  3 

3  +  2 

Ex.  2.        (1.) 

(2.) 

(3.) 

(4) 

(S.) 

(6-) 

5  +  3 

4+3 

3  +  9 

4+3 

7  +  3 

6  +  3 

3  +  5 

5  +  3 

7+3 

7+3 

4+3 

7+3 

6  +  1 

7  +  3 

6  +  3 

3  +  7 

3  +  4 

3  +  7 

6  +  3 

8  +  3 

3  +  9 

4+3 

7+3 

5  +  3 

5  +  3 

6  +  3 

7+3 

6  +  3 

8  +  3 

4+3 

6  +  3 

9  +  3 

6  +  3 

3  +  6 

3  +  4 

3  +  0 

i 

Ex.  3.      <1.) 

(2.) 

(3.) 

(4.) 

(«•) 

(6.) 

6  +  3 

3  +  3 

3  +  7 

6  +  3 

2  +  6 

3  +  3      1 

3  +  6 

7+3 

2  +  6 

3  +  2 

6  +  1 

2  +  3      1 

9  +  3 

2  +  3 

3  +  2 

2  +  8 

1  +  8 

4+3      ! 

8  +  3 

2  +  7 

1  +  5 

8  +  3 

8  +  3 

3  +  2      \ 

3  +  8 

6  +  2 

1  +  7 

9  +  3 

3  +  4 

2  +  9      i 

6  +  2 

2  +  3 

6  +  1 

4+2 

7  +  2 

3  +  2      \ 

i 

LESSON   XII. 

One  ship  and  4  ships  are  how  many  ? 

2  boats  and  4  boats  are  how  many  ? 

3  towers  and  4  towers  are  how  many? 

4  houses  and  4  houses  are  how  many  ? 

5  logs  and  4  logs  are  how  many? 

6  barrels  and  4  barrels  are  how  many? 

7  sea-gulls  and  4  sea-gulls  are  how  many  ? 

8  masts  and  4  masts  are  how  many  ? 

9  men  aild  4  men  are  how  many  ? 


ADDITION. 

17 

LESSON 

XIII 

(See  Manual,  Sec.  I. 

,  Exercise 

II.) 

!   C^PJ)  complete,  and  read  the  following 

tables : 

Ex.  1.        (1.) 

(2.) 

(3.) 

(■4.) 

(5.) 

(6.) 

4  +  2 

3  +  4 

5  +  4 

0+4 

1  +  3 

7+1 

2+4 

2+4 

4  +  2 

4  +  0 

4+2 

6  +  3 

3  +  2 

2  +  3 

2  +  3 

7+1 

2  +  3 

4+2 

2;fl 

3  +  1 

3  +  5 

8  +  0 

3  +  1 

7+3 

3+4 

4+2 

5  +  2 

8  +  1 

8  +  1 

6  +  2 

4  +  3 

4+4 

2+4 

3+1 

1  +  8 

2  +  3 

Ex.  2.       (1.) 

(2.) 

(3.) 

<4.) 

(5.) 

1 

(6.)          ! 

6+4 

4+6 

7+4 

2  +  4 

4  +  0 

6  +  4 

6+4 

4+7 

3  +  4 

0  +  4 

3  +  4 

4+6 

4+6 

4+3 

8+4 

4+0 

0  +  4 

6  +  2 

3  +  6 

4+8 

7+4 

8  +  4 

9  +  4 

6  +  4 

4  +  5 

4+9 

6  +  4 

9  +  4 

7+4 

4+6 

5  +  6 

4+7 

3  +  4 

3  +  4 

4+7 

3  +  4 

Ex.  a.    (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

6  +  4 

4+2 

5  +  4 

9  +  3 

0  +  4 

4+1 

IK      4+6 

2  +  4 

3  +  4 

4+3 

0  +  3 

1  +  0 

H   ^+^ 

6  +  4 

2+4 

2  +  2 

3  +  2 

0  +  1 

■      2+4 

8  +  2 

7+3 

3  +  3 

2  +  0 

1  +  1 

■      4+3 

2  +  4 

6  +  3 

4+4 

1  +  0 

2  +  2 

W      6  +  3 

2* 

6  +  4 

8  +  2 

7+3 

3  +  2 

3+3 

18 


ADDITION. 


LESSON    XIV. 

One  house  and  5  houses  are  how  many? 

2  lilies  and  5  lilies  are  how  many  ? 

3  pines  and  5  pines  are  how  many? 

4  windows  and  5  windows  are  how  many? 
5\lucks  and  5  ducks  are  how  many? 

6  islands  and  5  islands  are  11  islands. 
TJeaves  and  5  leaves  are  12  leaves. 

8  .flowers  and  5  flowers  are  13  flowers. 

9  doors  and  5  doors  are  14  doors. 


To  THE  Teacher. — Oral  questions  and  problems  referring  to  the 
above  and  following  illustrations  should  be  given  to  the  class.  (See 
Manual  Ex.  III.  Less.  IL)  The  pupils  should  be  required  to  ask 
questions  of  each  other  referring  to  the  objects  in  the  illustrations. 

Problems. — If  there  are  six  houses  and  each  house  has  one  door, 
how  many  doors  have  all  the  houses  ?  Five  of  the  doors  are  stand- 
ing open,  how  many  are  shut  ?  If  a  hunter  should  shoot  five  of  the 
ducks  in  the  pond,  how  many  would  escape?  If  a  little  girl  should 
pick  two  of  the  water  lilies,  how  many  would  remain  ?  Five  ducks 
and  3  ducks  are  how  many  ?  Three  trees  and  5  trees  are  how  many? 
Five  houses  and  two  houses  are  how  many  ?  Five  men  and  two  I 
men  are  how  many  ? 


ADDITION. 

19 

IiESSON 

XV. 

(See  Manual,  Sec  L, 

Exercise  11.) 

Copy,  complete,  and  read  tlie  following 

tables : 

Bx.  1.        (1.) 

(«•) 

(3.) 

(4.) 

(S.) 

(6.) 

5  +  6 

6  +  5 

6  +  5 

5  +  6 

6  +  7 

3  +  5 

6  +  3 

7+5 

5  +  6 

7+5 

7+5 

6  +  5 

5  +  Y 

8+5 

7+5 

8  +  5 

3  +  5 

6  +  6 

5  +  8 

9  +  5 

5  +  8 

5  +  6 

6  +  5 

7+5 

6  +  9 

8  +  5 

9  +  5 

5  +  7 

7+5 

3+5 

5  +  6 

3  +  5 

7+5 

5  +  6 

5  +  6 

6  +  5 

Kx.  8.        (1.) 

(2.) 

(3.) 

(4.) 

(S.) 

(6.) 

3  +  5 

5  +  2 

5  +  3 

6  +  2 

6  +  4 

4+3 

5  +  2 

6+2 

5  +  2 

8  +  1 

5  +  4 

7+2 

2+3 

7+2 

3  +  5 

7+2 

7+3 

4+3 

3  +  5 

5  +  3 

9  +  1 

7+3 

'6  +  4 

4+4 

4+2 

5  +  5 

8  +  2 

3  +  2 

5  +  5 

6  +  2 

4+5 

3  +  5 

7+3 

4+3 

9  +  1 

6  +  2 

Kz.  3.       (1.) 

(2.) 

(3.) 

(4.) 

(«•) 

(6.) 

7+4 

4+6 

7+5 

9  +  3 

4+6 

4+3 

4+5 

6+4 

5  +  6 

8  +  3 

3  +  2 

6  +  3 

6+4 

3  +  5 

7+2 

7+5 

3  +  1 

5  +  2 

8  +  5 

5  +  5 

9  +  3 

6  +  2 

6  +  7 

4  +  7 

7+6 

2  +  2 

4+3 

9  +  3 

6  +  8 

4+4 

7+3 

3  +  3 

9+1 

7+2 

3  +  7 

•6  +  5      I 

20  ADDITION. 


LESSON   XVI. 

One  branch  and  6  branches  are  7  branches. 

2  stones  and  6  stones  are  8  stones. 

3  cows  and  6  cows  are  9  cows. 

4  sheep  and  6  sheep  are  10  sheep. 

5  trees  and  6  trees  are  11  trees. 

6  lambs  and  6  lambs  are  12  lambs. 

7  feet  and  6  feet  are  13  feet. 

8  men  and  6  men  are  14  men. 

9  birds  and  6  bbds  are  15  birds. 


Problems.— If  3  cows  were  driven  home,  how  many  would  re- 
main in  the  pasture?  If  a  boy  should  drive  away  6  of  the  sheep, 
how  many  would  remain  ?  Since  1  cow  has  4  feet,  how  many  feet 
have  2  cows  ?  A  farmer  had  10  sheep,  he  sold  6  of  them,  how 
many  had  he  left?  There  are  9  cows  in  the  pasture,  6  of  the  cows 
have  been  milked ;  how  many  have  yet  to  be  milked  ?  Two  sheep 
and  3  sheep  are  how  many  ?  Two  cows  and  4  cows  are  how  many  ? 
Five  trees  and "4  trees  are  how  many?  How  many  feet  have  2 
sheep  ?  How  many  feet  have  4  sheep  ?  How  many  feet  have  8  sheep  'i 
How  many  horn%  have  three  cows?  How  many  horns  have  5  cows? 
How  many  horns  have  6  cows  ?  Five  boats  and  3  boats  are  how 
many  ?    Six  boys  and  5  boys  are  how  many  ? 


ADDITION. 

21 

1 

i 

i.x:ssoN 

XVII 

(See  Manual,  Sec.  I. 

Exercise  II.) 

Copy,  complete,  and  read  the  following 

tables : 

Ex.  1.        (1.) 

(2.) 

(3.) 

(4.) 

(«•) 

(6.) 

8  +  3 

3  +  3 

8  +  3 

6  +  2 

8  +  2 

8  +  2 

7  +  2 

6  +  5 

7+4 

8  +  3 

7  +  3 

7+2 

9  +  1 

2  +  2 

6  +  2 

7+4 

2  +  4 

3  +  6 

8  +  3 

1  +  1 

9  +  1 

5  +  4 

9  +  2 

7+2 

7+3 

7+3 

7+4 

4+4 

6  +  1 

4+2 

2  +  3 

6  +  2 

3  +  2 

2  +  2 

3  +  0 

4+1 

Ex.  a.      (X.) 

(2.) 

(3.) 

(4.) 

(«,) 

(6) 

6+5 

4+7 

4+6 

6  +  9 

8+6 

4+6 

6  +  6 

6  +  6 

6  +  7 

9  +  6 

3  +  6 

6  +  8 

3  +  6 

3+6 

6  +  8 

8  +  6 

6  +  7 

6  +  9 

4+6 

8  +  6 

6  +  3 

7+6 

7  +  6 

6  +  3 

9  +  6 

6  +  8 

6  +  9 

4+6 

9  +  6 

6+4 

7+6 

3  +  8 

6  +  7 

3  +  6 

8  +  6 

6  +  8 

Ex.  3.       (1.) 

(2.) 

(3.) 

(4.) 

(«•) 

(«•) 

8  +  6 

3  +  3 

8  +  3 

9  +  3 

4+7 

4+6 

6  +  7 

4+4 

5  +  7 

6  +  7 

6  +  3 

3  +  7 

3+4 

5  +  5 

6  +  9 

8  +  6 

8  +  3 

8  +  3 

6  +  3 

6  +  6 

3  +  7 

3  +  7 

4+7 

4+3 

4+4 

2  +  2 

8  +  6 

4+3 

6  +  7 

7+2 

3+3 

0  +  0 

4+7 

7+2 

4+7 

6  +  3 

J.ESSON  xvm. 

One  rake  and  7  rakes  are  8  rakes. 

2  forks  and  7  forks  are  9  forks. 

3  horses  and  7  horses  are  10  horses. 

4  men  and  7  men  are  11  men. 

5  scythes  and  7  scythes  are  12  scythes. 

6  jugs  and  7  jugs  are  13  jugs. 

7  cups  and  7  cups  are  14  cups. 

8  wagons  and  7  wagons  are  15  wagons. 

9  trees  and  7  trees  are  16  trees. 


pROB. — There  are  five  bunches  of  hay  on  one  side  of  the  wagon 
and  five  on  the  other,  how  many  on  both  ?  There  are  three  rakes, 
one  is  standing  against  a  tree,  the  rest  are  in  use ;  how  many  are  in 
use  ?  Four  rakes  and  5  rakes  are  how  many  ?  Five  baskets  and  6 
baskets  are  how  many  ?  Six  cups  and  5  cups  are  how  many  ?  Eight 
horses  and  3  horses  are  how  many?  Seven  trees  and  4  trees  are 
how  many  ?    Six  loads  of  hay  and  2  loads  are  how  many  ? 


ADDITION. 

23 

LSSSON 

ZIZ. 

(See  Manual,  Sec.  I., 

Exercise  II.) 

Copy,  complete,  and  read  the  following 

tables : 

Ex.  1.        (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

3  +  7 

3+4 

4+4 

3  +  1 

4  +  3 

8  +  3 

4+3 

9  +  3 

3  +  3 

7+2 

6  +  4 

4+2 

IK      6+4 

9  +  2 

2  +  2 

7+4 

8  +  4 

9  +  3 

H       ^+^ 

7  +  4 

1  +  1 

7+3 

5  +  3 

7  +  2 

R       8+4 

8  +  3 

0+0 

6  +  3 

7+4 

3  +  8 

j             6+4 

9  +  3 

0  +  1 

7+2 

9  +  3 

6  +  2 

i.  Ex,  a.     (1.) 

(2.) 

(3.) 

;4.) 

(«•) 

(6.) 

T+4 

7  +  8 

7+6 

9  +  7 

7+3 

8  +  7 

T  +  6 

7+9 

7  +  4 

7  +  9 

7+0 

6  +  7 

7+8 

7+6 

4+7 

3  +  7 

7+8 

3  +  7 

!            7+2 

7+2 

6  +  7 

6  +  7 

7+9 

7+3 

i            7+3 

7+3 

8  +  7 

4+7 

6  +  7 

7+8 

7+2 

7+0 

3  +  7 

4+7 

3  +  7 

7+3 

Ex.  3.       (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

7+8 

4+3 

4+6 

9  +  7 

6  +  7 

4+6 

^fc      6  +  7 

6  +  7 

6  +  7 

4+7 

6  +  8 

7  +  8 

^^B      3  +  8 

3  +  8 

8  +  7 

6  +  3 

3  +  4 

3  +  4 

^^B      9  +  7 

4+7 

3  +  8 

8  +  3 

7  +  2 

6  +  7 

l^m      ^'^'^ 

6  +  7 

3  +  7 

9  +  4 

4  +  3 

3  +  9 

P      *+'^ 

3  +  7 

4+3 

7  +  8 

6  +  7 

4+7 

^^^Hk 

24 


ADDITION. 


LESSON    XX. 

One  melon  and  8  melons  are  9  melons. 

2  peaches  and  8  peaches  are  10  peaches. 

3  cherries  and  8  clierries  are  11  cherries. 

4  bananas  and  8  bananas  are  12  bananas. 

5  clusters  and  8  clusters  are  13  clusters. 

6  leaves  and  8  leaves  are  14  leaves. 

7  plums  and  8  plums  are  15  plums. 

8  vases  and  8  vases  are  16  vases. 

9  vines  and  8  vines  are  17  vines. 


Problems. — Two  peaches  and  5  peaches  are  how  many?  Four 
pine-apples  and  6  pine-apples  are  how  many?  Eight  oranges  and 
4  oranges  are  how  many  ? 


! 
1 

ADDITION. 

25  k 

LESSON 

XXI. 

i 

« 

(See  Manual,  Sec.  I. 

Exercise  II.) 

Copy,  complete,  aud  read  the  following 

tables: 

Ex.  1.         Cl.) 

(2.) 

(3) 

(4.) 

(5.) 

(6.) 

6  +  7 

5  +  3 

8  +  3 

8  +  4 

1  +  1 

3  +  0 

5  +  8 

6  +  7 

7  +  2 

5  +  3 

3  +  3 

0  +  7     ! 

3  +  7 

8+4 

6  +  3 

6  +  7 

4  +  4 

8  +  0     ! 

4+6 

4+5 

5  +  3 

8  +  3 

4+4 

6  +  3 

4+3 

8  +  4 

7+4 

4+2 

5  +  5 

3  +  0 

4+7 

3+4 

6  +  3 

6  +  1 

6  +  6 

8  +  6 

Ex.  2.       (1.) 

<2.) 

(3.) 

(4.) 

(«.) 

(6.) 

:j           8  +  3 

8  +  7 

8  +  9 

8  +  6 

8  +  7 

8  +  7 

1             8  +  4 

9  +  9 

8  +  6 

8  +  7 

8  +  8 

8  +  6 

8  +  3 

8  +  3 

8  +  7 

8  +  4 

8  +  3 

8  +  8     1 

8  +  7 

8  +  6 

8  +  7 

8  +  9 

8  +  6 

8+4 

8  +  6 

8  +  7 

8  +  6 

8  +  7 

8  +  8 

8+6     1 

!             8  +  3 

8  +  8 

8  +  7 

8  +  6 

8  +  9 

8+9 

Ex.  3.        (1.) 

(2.) 

(3.) 

(4) 

(«.) 

(6.) 

8  +  8 

8  +  7 

6  +  7 

4+4 

2  +  0 

4+6 

8  +  3 

6  +  7 

9  +  3 

3  +  3 

7+0 

6  +  0 

3  +  7 

6  +  9 

8  +  7 

2  +  2 

8  +  9 

0+8 

;           3+4 

3  +  8 

8  +  9 

8  +  8 

0  +  8 

7+9 

1             7+6 

8  +  3 

6  +  9 

6  +  6 

7  +  0 

6  +  9 

'             8  +  9 

3 

7+4 

7+8 

3  +  3 

6  +  8 

3+8 

26 


ADDITION. 


LESSON  xxn. 

One  rock  and  9  rocks  are  1 0  rocks. 

2  trees  and  9  trees  are  11  trees. 

3  wheels  and  9  wheels  are  12  wheels. 

4  carts  and  9  carts  are  13  carts. 

5  limbs  and  9  limbs  are  14  limbs. 

6  sheds  and  9  sheds  are  15  sheds. 

Y  icicles  and  9  icicles  are  16  icicles. 

8  posts  and  9  posts  are  17  posts. 

9  crows  and  9  crows  are  18  crows. 


Problems.— If  there  are  14  icicles  on  the  shed,  and  there  are  7  on 
one  side  of  the  post,  how  many  are  on  the  other  ?  There  were  3 
crows  sitting  on  the  tree,  two  have  flown  away ;  how  many  re- 
main ?  Four  crows  and  5  crows  aro  how  many  ?  Six  carts  and  3 
carts  are  how  many  ?  Nine  sheds  and  4  sheds  are  how  many?  Four 
wheels  and  8  wheels  are  how  many  ?  Eight  posts  and  7  posts  are 
how  many?  Five  trees  and  7  trees  are  how  many  ?  Nine  rocks 
and  5  rocks  are  how  many  ?  Four  branches  and  8  branches  are  how 
many  ?  Nine  snow-drifts  and  3  snow-drifts  are  how  many  ?  Three 
fences  and  5  fences  are  how  many  ? 


ADDITION. 

27 

I.ESSON 

XXIII 

• 

(See  Manual,  Sec.  I. 

,  Exercise  11) 

Copy,  complete,  and  read  the  follomng 

tables : 

Ex.  t .         (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

4  +  3 

4+3 

4+6 

6  +  7 

4+6 

4+3 

7  +  3 

7  +  2 

7+1 

6  +  3 

7+4 

3+8    : 

6  +  1 

6  +  7 

6  +  6 

5  +  3 

3  +  4 

8  +  3 

4+2 

5  +  7 

5  +  6 

8  +  6 

4+3 

9  +  3 

6  +  8 

3  +  2 

8  +  3 

9  +  7 

6  +  7 

4+8 

3  +  2 

Q  +  Q 

4  +  7 

7+7 

6  +  4 

7  +  1 

Ex.  2.        (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

9+4 

4+6 

4+6 

8  +  6 

9  +  6 

4+3 

9  +  3 

7+3 

7  +  8 

7+9 

9  +  8 

9  +  9 

6  +  9 

3+7 

8  +  9 

9  +  6 

3  +  2 

6  +  9      ! 

3+2 

8  +  6 

6+4 

9  +  4 

9  +  8 

3+4      1 

4+6 

6+4 

3  +  4 

9  +  8 

6  +  4 

9  +  2      i 

5  +  3 

3  +  7 

7+2 

3  +  7 

3  +  8 

4+3 

Ex.  3.       (1.) 

(2) 

(3.) 

(4.) 

(«•) 

(6.)            1 

2  +  2 

4+2 

5  +  6 

9  +  9 

8  +  8 

4  +  6 

1  +  1 

4+6 

6  +  7 

7+7 

3  +  9 

7+3      1 

6  +  6 

6  +  2 

8  +  8 

6  +  6 

7+9 

3  +  8      i 

8  +  9 

0  +  0 

9  +  9 

4+4 

6  +  8 

3  +  8      1 

9  +  9 

8  +  0 

6  +  5 

2  +  2 

3  +  8 

6  +  7 

7+7 

0  +  9 

3  +  3 

1  +  1 

2  +  4 

6  +  7      1 

i 

LESSON    XXIV. 

One  load  from  1  load  leaves  how  many  ? 
1  fork  from  2  forks  leaves  how  many  ? 
1  horse  from  3  horses  leaves  how  many  ? 
1  cow  from  4  cows  leaves  how  many  ? 
1  tree  from  5  trees  leaves  how  many  ? 
1  sheep  from  6  sheepTleaves  how  many  ? 
1  sheaf  from  7  sheavQs  leaves  how  many? 
1  post  from  8  posts  leaves  how  many  ? 
1  bird  from  9  birds  leaves  how  many  ? 

^-!^^ 


8UBTEACTI0N. 

29, 

LESSON 

XXV. 

* 

(See  Manual,  Sec.  I 

,  Exercise  III.) 

Copy,  complete 

and  read  the  following 

tables : 

Ex.  1. 

Model. 

(1) 

(2) 

(3) 

C4.)            1 

6-1=5 

8-1 

9-1 

8-1 

3-1     1 

7-1=6 

6-1 

7-1 

6-1 

7-1     1 

IK 

9-1=8 

3-1 

8-1 

8-1 

6-1     1 

^^K 

7-1=6 

4-1 

6-1 

2-1 

8-1 

^^B 

5-1=4 

9-1 

1-1 

2-1 

3-1 

H 

3-1=2 

6-1 

4-1 

4-1 

4-1 

iff^. 

Model. 

(1) 

(2.) 

(3.) 

(4.) 

3-1=2 

4-1 

5-1 

4-1 

5-1 

!■ 

5  +  1=6 

3-1 

6  +  1 

3  +  1 

6  +  1 

■ 

6+1=7 

7-1 

7+1 

6-1 

7-1 

m 

3-1=2 

6-1 

3-1 

7-1 

8  +  1 

3+1=4 

3-1 

6  +  1 

4-1 

0+1 

5-1=4 

4-1 

5  +  1 

4+1 

4-1 

Ex.  3. 

(1.)             (2)            (3.) 

(4) 

(5) 

(6) 

4+1    4- 

1     9-1 

1-1 

4-1 

1  +  9 

8+1     6+1     6-1 

1  +  1 

3  +  1 

9-1 

4-1     3+1     8-1 

1  +  0 

4+0 

8  +  7 

3-1    4- 

1    7+1. 

.    1  +  8 

5-0 

1  +  8 

6  +  1     7- 

1     9-1 

8-1 

6  +  1 

4-1 

2  +  1     9- 

1     3-1 

3-1 

9-1 

9-1 

*  I^ote  for  tJie  Teacher 

\— Illustrate  ttie  meaning 

and  the  use  of  the  sign  || 

jf  subtraction  (-)  in  the  following  Exercises. 
3* 

LESSON    XXVI. 

Two  boys  from  2  boys  leave  how  many  ? 
2  barrels  from  3  barrels  leave  how  many  ? 
2  cages  from  4  cages  leave  how  many  ? 
2  rabbits  from  5  rabbits  leave  how  maoy  ? 
2  turnips  from  6  turnips  leave  how  many  ? 
2  chicks  from  7  chicks  leave  how  many  ? 
2  branches  from  8  branches  leave  how  many  ? 
2  birds  from  9  birds  leave  how  many  ? 
'  2  ears  from  10  ears  leave  how  many  ? 


SUBTRACTION. 

31 

■ 

LESSON    XZVII 

vm 

(See  Manual,  Sec.  I., 

Exercise  III.) 

^opy7  complete,  and  read  the  foUomng 

tables : 

Ex.  1.        (1.) 

(2.) 

(3.) 

<4.) 

(5.) 

(6.) 

3-2 

4-2 

4-2 

4-2 

4-2 

4-2 

6-2 

6-2 

6—2 

6-2 

6-2 

8-2 

H      4-2 

7-2 

3-2 

8-2 

4-2 

7-2 

■      8-2 

3-2 

4-2 

4-2 

3-2 

3-2 

■      5-2 

4-2 

6-2 

3-2 

4-2 

4-2 

B 

6-2 

4-2 

6-2 

6-2 

5-2 

Ex.  2.        (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

2-2 

4-^2 

4-2 

4-2 

5-2 

4-2 

4-2 

6-2 

7-2 

6-2 

7-2 

6-2 

6-2 

4—2 

4-2 

3-2 

3-2 

3-2 

3-2 

3-2 

6—2 

4-2 

6-2 

2-2 

6-2 

8-2 

8-2 

6—2 

4—2 

3-2 

3-2 

6-2 

3-2 

4-2 

3-2 

6-2 

Ex.  3.        (1.) 

(2.) 

(3.) 

(4.) 

(«■) 

(6.) 

2-2 

6-2 

4-2 

9-2 

6-2 

9  +  2 

8  +  2 

8-2 

7+2 

7+2 

8  +  2 

7  +  2 

7+2 

4+2 

4-2 

8-2 

2-2  10+2 

4-2 

7+2 

8  +  2 

6  +  2 

7+2  11-2 

6  +  2 

3-2 

7-2 

8  +  2  11  +  2  12  +  2      1 

4-2 

8  +  2 

6  +  2 

4-2  11  +  2 

7+2 

1 

LESSON   XXIX. 

3  books  from  3  books  leave  how  many  ? 

3  pictures  from  4  pictures  leave  how  many  ? 

3  globes  from  5  globes  leave  how  many  ? 

3  chairs  from  6  chairs  leave  how  many  ? 

3  books  from  7  books  leave  how  many  ? 

3  pictures  from  8  pictures  leave  how  many  ? 

3  busts  from  9  busts  leave  how  many? 

3  books  from  10  books  leave  how  many  ? 

3  pictures  from  11  pictures  leave  how  many? 

3  busts  from  12  busts  leave  how  many  ? 


STXBTBACTION. 

33 

LESSON 

XZIX 

(See  Manual,  Sec  I., 

Exercise  IIL) 

Copy,  complete,  and  read  the  following 

tables : 

KT.  1.         (1.)             (2.)             (3.) 

(4.) 

(5.) 

(6-) 

4_3     8-3    4-3 

6-3 

4-3 

4-3 

7-3     7-3     6-3 

4-3 

7-3 

8-3 

mm      8    3    4    3    7    3 

8-3 

6-2 

4-3 

■      4-3    5-3     8-3 

7-3 

8-3 

7-3 

H      6-3     7-3     7-2 

4-8 

4-3 

6-3 

H      4-3     4-3    4-3 

3-3 

4-3 

9-3 

Ex.2.        (1.)           (a)           (3.) 

(4.) 

(5.) 

(6.) 

3-2    4-3    4-3 

6-3 

9-6 

8-3 

8-2    5-3    3-3 

3-3 

11-3 

7-3 

7-3  12-3     7-3 

7-3 

8-3 

6-3 

8-3  11-3  11-3 

11-3 

6-3 

11-3 

9_3    9-3  12-3 

8-3 

7-4 

7-3 

6-8  11-3  10-3 

6-3 

3-3 

6-3 

Kl.  3.  .    (1.)            (2.)             (3.) 

(4.) 

(5.) 

(6.) 

3+2    4-1     3+7 

6  +  3 

8-3 

4-2 

4+3    3_2    4+2 

7-3 

4+3 

7+3 

6-3    7+2     7-3 

4+2 

7-3 

8  +  3 

7-3    3+7    3+8 

8-2 

6  +  7  12-3 

3+7    9-3    7+3 

6  +  1 

5-2 

9  +  3 

4+3     7-2  11-2 

3-1 

4+3 

7+3 

LESSON  XXX. 

4  houses  from  4  houses  leave  no  houses. 

4  roses  from  5  roses  leave  1  rose. 

4  gates  from  6  gates  leave  2  gates. 

4  girls  from  7  girls  leave  3  girls. 

4  kittens  from  8  kittens  leave  4  kittens. 

4  dishes  from  9  dishes  leave  5  dishes. 

4  stools  from  10  stools  leave  6  stools. 

4  cats  from  11  cats  leave  7  cats. 

4  bushes  from  12  bushes  leave  8  bushes: 

4  windows  from  13  windows  leave  9  windows. 


*  Problems.— There  are  two  stools,  each  has  4  legs ;  how  many 
legs  have  both  ?  There  are  7  little  girls  at  a  picnic,  4  of  them  re- 
turn; how  many  remain?  There  are  8  roses  on  the  rose-bush; 
Henry  picked  4  of  them ;  how  many  remain  ?  etc. 

*  ITiese  and  the  following  problems  are  not  for  the  pupils  to  tludy,  but 
for  the  teacher  to  dictate  to  the  class. 


8UBTEACTI0N. 

35 

LESSON 

XXXI. 

(See  Manual,  8eo.  I., 

Exercise  III.)    . 

Copy,  complete,  and  read  the  following 

tables : 

£x.  1. 

(1.) 

(2.) 

(3) 

(4.)             <5.) 

(6.) 

6-4 

5-4 

8-4 

7-4    9-4 

8-4 

■ 

7-4 

6-4 

6-4 

8-4    8-4 

7-4 

B 

8-4 

9-4 

8-4 

6-4    6-4 

6-4 

■ 

9-4 

4-4 

7_4  13_4    8-4 

8-4 

p 

8-4 

6-4 

6-4 

4-4    9-4 

8-4 

6-4 

7-4 

9-4 

7-4  11-4 

7-4 

Ex.  8. 

(1) 

(2.) 

(3.) 

(4.)             (5.) 

(6.) 

4-3 

8-4 

8-4 

7-4  13-4  11-4 

8-4 

7-4  11-4 

6-4  10—4  13—4 

7-4  11-4  12-4 

8-4    8-4  10-4 

9-4 

9-4 

13-4 

4-4  11-4 

9-4     1 

6-4 

8-4  11-4 

8-4    7-4  12-4     ! 

12-4  10-4 

8-4 

7-4    6-4 

4-4     ! 

e:x.  3. 

(1.) 

(2.) 

(3.) 

(4.)           (5.) 

(6.) 

8+4 

3+4 

8+4 

8-4    9+4 

4-4 

4-4 

7+4 

4-4 

8+4    7+4 

8  +  6 

6-4 

6-4 

8-4 

7-4  13-4 

4-4 

7+4 

8-4 

8+4 

3  +  4  10-4 

8+4 

3+4 

9+4 

5+4 

4+6  11-4 

7+4 

6  +  7 

6+4 

7-4 

13-4    6+4  13-4 

LESSOX    XXXIJ. 

5  saws  from  5  saws  leave  no  saws. 

5  boxes  from  6  boxes  leave  1  box. 

5  planes  from  7  planes  leave  2  planes. 

5  hammers  from  8  hammers  leave  3  hammers. 

5  chisels  from  9  chisels  leave  4  chisels. 

5  boards  from  10  boards  leave  5  boards, 

5  benches  from  11  benches  leave  6  benches. 

5  axes  from  12  axes  leave  7  axes. 

5  rules  from  13  rules  leave  8  rules. 

5  cages  from  14  cages  leave  9  cages. 


Problems.— A  little  boy  agreed  to  make  8  bird-cages ;  he  has  4  of 
them  done;  how  many  has  he  yet  to  make  ?  He  had  11  chisels, 
but  broke  3  of  them  ;  how  many  had  he  left?  He  used  5  pieces  of 
board,  and  has  4  left ;  how  many  liad  he  at  first  ?  He  had  8  augers; 
he  loaned  three  of  them  ;  how  many  had  he  left?  etc.  ,' 


SUBTRACTION. 

37 

1 

LESSON    ZXXIII. 

■ 

■ 

(See  Manual,  Sec.  I., 

Exercise  III.) 

Copy,  complete,  and  read  the  following 

tables ;   ; 

Ex.  1. 

(1.) 

(2.) 

(3.) 

(4.) 

(6.) 

(6.) 

6-5 

4-5 

10-5 

8-5 

14-5 

14-5 

■ 

7-5 

6-5 

8—5 

7-5 

9-5 

6-5     1 

9-5 

7-5 

7-5 

13-5 

7-5 

8-5 

10-5 

8-5 

6-5 

14-5 

6-5 

9-5 

8-5 

6-5 

8-5 

6-5 

8-6 

11-5 

7-5 

5-5 

9-5 

5-5 

13-5 

6-5 

Ex.  2. 

(1-) 

(2.) 

(3.) 

(4.) 

(5.) 

(6.) 

1-5 

11-5 

13-5 

14-5 

14-5 

7-5     1 

7-5 

7-5 

6-5 

7-5 

8-5 

6-5 

■ 

6-5 

11-5 

8-5 

8-5 

6-5 

7-5 

9-5 

12-5 

8-5 

8-5 

8-5 

9-5 

8-5 

13-5 

7-5 

13-5 

7-5 

9-5 

13-5 

14-5 

6-5 

6-5 

8-5 

7-5 

Ex.3. 

(I-) 

(2.) 

<3.) 

(4.) 

<«•) 

(6.) 

3  +  5 

4  +  5 

8  +  1 

8-2 

5  +  6 

5-5 

7+5 

7-5 

9  +  2 

3  +  8 

7+4 

7-4 

9-5 

3  +  5 

7-2 

7-5 

7-2 

4-4 

13-5 

2  +  5 

7  +  2 

2  +  5 

7+2 

0-0    ! 

14-5 

5-2 

13-4 

7-2 

4+2 

1~0 

4 

5  +  3 

7-5 

7-4 

3+4 

2  +  3 

1-1 

38 


SUBTRACTION. 


LESSON   XXXIV. 

6  tents  from  6  tents  leave  no  tents. 

6  Indians  from  7  In^'ians  leave  1  Indian. 

6  canoes  from  8  canoes  leave  2  canoes. 

6  paddles  from  9  paddles  leave  3  paddles. 

6  trees  from  10  trees  leave  4  trees. 

6  bushels  from  11  bushels  leave  5  bushels. 

6  birds  from  12  birds  leave  6  birds. 

6  bows  from  13  bows  leave  7  bows. 

6  arrows  from  14  arrows  leave  8  arrows. 

6  spears  from  15  spears  leave  9  spears. 


Problems.— A  party  of  12  Indians  went  to  hunt ;  6  of  them  re- 
turned ;  how  many  were  still  away  ?  In  a  village  there  were  11 
wigwams,  all  but  3  were  blown  down ;  how  many  were  blown 
down  ?  There  are  8  Indians  in  the  boats,  and  1  is  standing  on  th( 
shore ;  how  many  are  there  in  all  ?  etc. 


SUBTEACnON. 

39 

LESSON    XXXV 

(See  Manual,  Sec.  I.,  Exercise  III.) 

Oopj,  complete,  and  read  the  following 

tables : 

Ix.  1. 

a.) 

(2.)          (3 )             (4.) 

(5.) 

(6.) 

14-6 

9_6  15-6  14-6 

9-6 

14-6 

14-6 

7-6  11-6     7-6 

8-6 

13-6 

15-6 

9-6     8-6     8-6 

7-6 

7-6 

11-6 

12-6  15-6  14-6 

10-6 

8-6 

14-6 

13-6  13-6  15-6 

13-6  14-6     j 

13-6 

13-6  11-6  12—6 

15-6 

9-6 

Sx.  2 

.     (1.) 

(2.)             (3.)             (4.) 

(S.) 

(6.) 

5  +  6 

7-6    5-3    5  +  7  15-6 

8  +  6 

7-6 

8-6     5-3     .'-3 

13—6 

7+6 

4+2 

8  +  2     8  +  3  13   -5 

14-6 

7-6 

m 

8  +  2 

7+6     6+3  15-3 

8-0 

5-2 

3  +  1 

3-2     7-2    0-0 

7+3 

3-1 

6  +  1 

3+6    6-4    7-3 

5  +  3 

6-6 

Sx.  3. 

(1-) 

(2.)              (3.)            (4.) 

(5.) 

(6.) 

7-6 

8  +  6     9  +  6  15-6 

13-6 

11-6 

9  +  6  13-6  11-6     9-5 

7  +  5  12-6     i 

8  +  6  11-6  13-6  11-6 

6  +  6  13—6     i 

* 

15-6 

15-6  14-6  10-6 

14-6 

9+6 

13-6 

12-6  13-6  13-6 

13-6 

15-6 

11-6 

15-6  10-6  14-6 

9  +  6 

6  +  6 

LESSON    XXXVI. 

7  turkeys  from  7  turkeys  leave  how  many  ? 

7  turkeys  from  8  turkeys  leave  how  many  ? 

7  chicks  from  9  chicks  leave  2  chicks. 

7  doves  from  10  doves  leave  3  doves. 

7  cows  from  11  cows  leave  4  cows. 

7  hens  from  12  hens  leave  5  hens. 

7  swallows  from  13  swallows  leave  6  swallows. 

7  pails  from  14  pails  leave  7  pails. 

7  sheds  from  15  sheds  leave  8  sheds. 

7  barns  from  16  barns  leave  9  barns. 


Problems.  —  There  are  6  chicks  and  1  chirk  in  a  brood;  how 
many  chicks  are  there?  There  are  13  swallows  in  a  flock,  7  of 
them  have  flown  away ;  how  many  remain  ?  etc. 


" 

SUBTRACTION. 

41 1 

1 

LESSON    ZXXVII. 

i 

(See  ManuaV  Sec.  I. 

Exercise  III.) 

\ 

Copy,  complete,  and  read  the  following 

tables : 

fix. 

1.        (1.) 

(2.)            (3.) 

(4.)            (5) 

(6) 

10-7 

11-7  14-7 

14-7    7- 

-7 

8-7 

16-7 

8-7  16-7 

13-7  16- 

-7 

9-7 

13-7 

9-7  15-7 

16-7    8- 

-7 

13-7     i 

11-7 

11-7    8-7 

15-7    9- 

-7  16-7      ; 

16-7 

14-7  16-7 

8-7  16- 

-7  15-7     j 

! 

14-7 

16—7  13-7 

9-7  15- 

-7 

8-7 

Ejc. 

2.         (1.) 

(2.)             (3.) 

(4.)              <5.) 

(6-> 

7-1 

74-7  13_7  15-7  10- 

-7  15-7 

7  +  7 

9  +  7  14_7  16-7  16- 

-7  16-7 

7-3 

9-7  15-7 

13-7  lo- 

-7 

11-7    '1 

7+4  10  +  7  16-7 

ll -7  13- 

-6 

12-7 

7  +  5 

11-7  15-7  12-7  11- 

-7 

9-7 

_7-6 

12-7    7+0 

11-7  14- 

-7 

7+7 

Bx. 

3.       (1.) 

(2.)              (3.) 

(4-)              («•)      , 

(6.) 

7+2 

13_6     8  +  3 

8+3     8+7 

4+5 

7-1 

3+6    7-2 

7+1     5+9 

7  +  7 

8-1 

4+6     8-3 

5-2    6- 

-3 

3  +  8 

4-2 

7+5    7-4 

5  +  2     9- 

-7 

9-7 

2  +  2 

5-2     6+2 

9-7  13- 

^7 

3-1 

5  +  2 

5+2    4+3 

6  +  6  16- 

-7 

8-2 

1 

4»    - 

% 

. 



42 


SUBTRACTION. 


LESSON   XXXVII. 

Eight  trees  from  8  trees  leave  no  trees. 

8  ropes  from  9  ropes  leave  1  rope. 

8  boys  from  10  boys  leave  2  boys. 

8  girls  from  11  girls  leave  3  girls. 

8  bouses  from  12  bouses  leave  4  bouses. 

8  barns  from  13  barns  leave  6  barns. 

8  caps  from  14  caps  leave  6  caps. 

8  flowers  from  15  flowers  leave  7  flowers. 

8  bushes  from  16  bushes  leave  5  bushes. 

8  horses  from  17  horses  leave  9  horses. 


Problems. — John  swung  his  little  sister  5  minutes  and  his  littie 
brother  7  minutes  ;  how  many  minutes  did  he  swing  both  ? 


StTBTEACTION. 

43 

LESSON 

XXXIX. 

(See  Manual,  Sec.  I., 

Exercise  IIL) 

Copy,  complete,  and  read  the  following 

tables : 

Ex.  I.        (1.) 

(2.) 

(3.) 

(4.)              (5.) 

(6.) 

9-8 

8-8 

11-8 

16-8  16-8 

17-8 

17-8  17-8 

16-8 

13-8  13-8 

13—8 

IB    16-8 
'^    13-8 

13-8 

13-8 

15-8  12-8 

12-8     i 

16-8 

14-9 

14-8  17-8 

9-8 

11-8 

15-8 

17-8 

11—8  12-8 

13-8 

_17-8 

12-8 

18-8 

13-8  13-8  17-8     ' 

i 

Bx.  a.      (1.) 

(2.) 

(3.) 

(4.)              (5.) 

(6.) 

17-8 

14-8 

9-8 

8-2  13-8 

14-8 

11-8 

13-8 

8  +  7 

8  +  1  15-8  17-8 

16-8 

12—8 

8  +  6 

8-0  16-8 

16-8 

15-8 

10-8 

8-5 

11-8  13-8 

11-8 

14-8 

11-8 

8+4  13-8  11-8 

12-8 

13-8 

8  +  8 

8+3  15-8  13-8 

13-8 

Ex.  3.       (1.) 

(2.) 

(3.) 

(4.)             (5.) 

(6.) 

17-8 

6  +  9 

5  +  8 

8-8     6+8 

8  +  0 

16-8 

11-8 

13-8 

8+8     9-8 

0+8 

13-8 

8-8 

6  +  8 

3  +  8  13-8 

8-8 

14-8 

8  +  8  14-8 

13-8  17-8 

8-0 

17-8 

10-8 

4  +  6  14-8     6+8 

7+8 

13-8 

9  +  8 

5  +  7 

4+7    5+8 

8  +  8 

LESSON    XL. 


9  mills  from  9  mills  leave  no  mills. 

9  trees  from  10  trees  leave  1  tree. 

9  men  from  11  men  leave  2  men. 

9  boats  from  12  boats  leave  3  boats. 

9  do^s  from  13  dogs  leave  4  dogs. 

9  wheels  from  14  wheels  leave  5  wheels. 

9  doors  from  15  doors  leave  6  doors. 

9  bridges  from  16  bridges  leave  7  bridges. 

9  fish-poles  from  17  fish-poles  leave  8  fish-poles. 

9  posts  from  18  posts  leave  9  posts. 


Problems- — A  man  caught  8  fishes  at  one  time  and  6  at  another ; 
how  many  did  he  catch  in  all  ?  If  a  mill  grinds  8  bushels  of  corn 
and  12  bushels  of  wheat ;  how  much  more  wheat  does  it  grind  than 
corn  ? 


i , 

STTBTEACnON. 

45 

X.BSSON    XX.I. 

(See  Manual,  Sec.  I.,  Exorcise  III.) 

;   Copy,  read, 

and  complete  the  following 

tables : 

Ex.  1.        (1.) 

(2.)           (3.)              (4.) 

(5.) 

(6.) 

9-9 

•9-3  15-9  13-9 

14-9 

15-9 

9-8 

9_2  18-9  14-9 

13-9 

16-9 

9-.T 

9-1  17-9  16-9 

18-9 

18-9     i 

j             9-6 

9-0  16-9  18-9 

16-9 

13-9 

1             9-5 

10-9  18-9  13-9 

17-9 

15-9 

1              9-4 

11-9  17-9  10-9 

9-9 

18-9 

Ex.  2.       (1.) 

(2.)             (3.)             (4.) 

<5.) 

C6.) 

8  +  7 

4-3    4+6     3+7 

4  +  6 

4  +  6 

5  +  6 

9-4    3+7     8+9 13-9 

8  +  6 

3-2 

9  +  3  18-9     3-1 

14-8 

9+1  : 

8-4 

8  +  7  17-8    0  +  1 

7+8 

3  +  1 

9-3 

4+3    4+7     8+0 

9  +  5 

5-2 

7  +  6 

8+7    6+9     9-3 

11-9 

7-2 

Ex.  3.        (1.) 

(2.)               (3.)             (4.) 

(«.) 

(6.)             ' 

9  +  9 

9+1     8+8     4+9 

15-9 

4+8 

13-9 

18-9     7+9     7  +  8 

7+9 

7  +  9 

18-9 

17-9  ii_9     9_8 

8  +  9 

6  +  9 

3  +  7  13-9     8-9  17-9 

17-9 

13-9 

7+9 

6  +  9  17—9  11-9 

16-9 

15-9 

18-9 

3  +  9  13-9  13-9 

13-9 

17-9     1 

»^ 

Once  2 

2  times 

3  times 

4  times 

5  times 

6  times 

7  times 

8  times 

9  times 


LESSON  XLII. 

ducks  are  2  ducks. 
2  men  are  4  men. 
2  ducks  "are  6  ducks. 
2  dogs  are  8  dogs. 
2  guns  are  10  guns. 
2  trees  are  12  trees. 
2  ducks  are  14  ducks. 
2  islands  are  16  islands. 
2  logs  are  18  logs. 


MULTIPLICATION. 

47 

LESSON    XIiIII 

.* 

(See  Manual,  Sec.  I.,  Exercise  IV.) 

Copy,  complete,  and  read  the  following 

tables : 

Ex.  1.           Model.                (1.)              (2.) 

(3.) 

(4) 

:          '    4x2=^8      2x2      2x2 

5x2 

4x2 

3x2=6      0x2      3x2 

4x2 

5x2 

2x2=4      3x2      4x2 

1x2 

3x2 

1x2=2      2x3      1x2 

1x1 

2x2 

5x2=10    3x2      3x2 

2x2 

4x2 

4x2=8      4x2      4x2 

3x2 

1x2 

Kx.  2.          Model.              (1.)               (2.) 

(3.) 

(4-) 

3x2=6      6x2      1x2 

6x2 

4x2 

4x2=8      7x2      7x2 

7x2 

3x2 

5x2=10    6x2      3x2 

6x2 

9x2 

7x2=14    7x2      6x2 

3x2 

6x2 

2x2=4      4x2      8x2 

8x2 

9x2 

0x2=0      4x0      3x2 

1 

6x2 

3x2 

Bx.  3.        (1.)            (2.)           (3.)           (4.) 

(«•) 

(6.) 

3x2     5+2     5x2    4+2 

0x6 

7+2 

2+3     7-2     5-2     6+2 

6x0 

4-2 

4x2    3x2     5+2    2+6 

6-0 

7  +  2 

6-2     7x2     2+5     2x6 

6  +  0 

9-1 

2x6     6-2    3+0     6x2 

0  +  6 

8-2 

4-2    4+2    0+3     6-0 

9x2 

4-2 

j       *  Note  for  the  ^(gac^er.— Illustrate  the  meaning  and  tlie  use  of  the  sign  J 

of  multiplication  (  x  )  in  the  following  Exercises. 

" ^^^^ 

Once  3 

2  times 

3  times 

4  times 

5  times 

6  times 

7  times 

8  times 

9  times 

LESSON  XLIV. 

ladders  are  3  ladders. 

3  poles  are  6  poles. 

3  windows  are  9  windows. 

3  men  are  12  men. 

3  poles  are  15  poles. 

3  window^s  are  18  windows. 

3  hods  are  21  hods. 

3  timbers  are  24  timbers. 

3  bricks  are  27  bricks. 


Pkoblems.— If  a  man  carry  9  bricks  in  his  hod  at  one  load,  how 
many  bricks  can  he  carry  in  going  3  times  ?  There  are  9  windows 
in  one  story ;  how  many  windows  in  3  stories  ? 


MULTIPLICATION. 

49 

LESSON 

XLV. 

1 

(See  Manual,  Sec.  I., 

Exercise  IV.) 

i   Copy,  complete,  and  read  the  following 

tables : 

Ex.  1. 

(1.) 

(2.) 

(3.) 

(4.) 

ca.j 

(6.) 

5x3 

1x3 

2x3 

4x3 

6x3 

3x6     I 

4x3 

7x3 

3x3 

5x3 

7x3 

3x2     1 

3x3 

5x3 

0x3 

4x3 

8x3 

3x5 

2x3 

2x3 

5x3 

1x3 

5x3 

5x3 

4x3 

4x3 

8x3 

0x3 

7x3 

4x3 

5x3 

2x3 

6x3 

3x0 

6x3 

2x3 

Ex.  2. 

(1.) 

(2.) 

(3.) 

(4-) 

(5.) 

«5.) 

i 

4x3 

5x3 

7x3 

1x3 

5x3 

6x3 

5x3 

7x3 

6x3 

9x4 

7x3 

7x3 

7x3 

6x3 

4x3 

6x3 

6x3 

6x3 

8x3 

3x3 

0x3 

7x3 

8x3 

8x3 

4x3 

7x3 

6x3 

5x3 

7x3 

6x3 

6x3 

9x3 

7x3 

6x3 

9x3 

9x3 

Ex.3. 

(1.) 

(2.) 

(3.) 

(4.) 

(5.) 

(6-)          '' 

3x3 

4x3 

3  +  0 

7  +  3 

4+3 

4x3 

4x3 

4-3 

0  +  3 

3x7 

3  +  3 

4-3     ! 

12-3 

4+3 

3-0 

5  +  3 

3-3 

7+3     i 

7x3 

7x8 

3  +  0 

3x5 

7-3 

7-3   -j 

7+3 

7-3 

3x0 

6x3 

11-3 

3  +  3     ' 

7-3 

7  +  3 

0x3 

8x6 

10-3 

3-3 

,i 

— 

50 


MULTIPLICATION. 


4  times  2  pigs  are  8  pigs. 


4  times  4  goats  are  16  goats. 


5  times  5  ducks  are  25  ciucks. 


LESSON   XLYI. 

Once  4  goats  are  4  goats. 

2  times  4  feet  are  8  feet. 

3  times  4  nests  are  12  nests. 

4  times  4  birds  are  16  birds. 

5  times  4  pigs  are  20  pigs. 

6  times  4  kids  are  24  kids. 

7  times  4  wings  are  28  wings. 

8  times  4  eggs  are  32  eggs. 

9  times  4  ears  are  36  ears. 


'' 

1 

MtTLTIPLIOATION. 

51 

LBSSON 

SLVIl 

^ , 

(Sec  Manual,  Sec.  I., 

Exercise  IV.) 

Copy,  read, 

and  complete 

the  following  tables :   j 

!bx.  1. 

(1-) 

(2.) 

(3.) 

(4.) 

(a.) 

(6.) 

3x4 

6x4 

6x4 

3x4 

6x4 

4x4 

2x4 

2x4 

7x4 

2x4 

3x4 

6x4 

0x4 

7x4 

3x6 

4x4 

7x4 

3x4 

1x4 

9x4 

8x4 

0x4 

3x4 

7x4 

8x4 

3x4 

2x4 

3x4 

6x4 

6x4 

3x4 

2x4 

7x4 

3x4 

2x4 

3x4 

Ex.  2. 

(1.) 

(2.) 

(3.) 

(4.) 

(6.) 

(S.) 

3x4 

5x4 

8x4 

6x4 

8x4 

5x4 

4x4 

3x4 

7x4 

5x4 

6x4 

7x4 

7x4 

7x4 

8x4 

7x4 

8x4 

8x4 

9x4 

5x4 

0x4 

3x4 

9x4 

3x4 

6x4 

8x4 

9x4 

6x4 

7x4 

7x4 

1 

4x4 

7x4 

7x4 

7x4 

6x4 

6x4 

Kt.3. 

(1.) 

(2.) 

(3.) 

(4.) 

(5.) 

C6.) 

3+4 

5x4 

6  +  4 

8-4 

6x4 

2+4 

3x4 

5-4 

6-4 

8-0 

6  +  4 

2-1 

3-0 

5+4 

6x4 

0x8 

13-4 

8x4 

4x4 

13-4 

11-4 

8x0 

7x4 

8x4 

7x4 

7+4 

8-4 

5-3 

8  +  4 

8+4 

4x4 

7-4 

6+4 

4x7 

7+4 

8x3 

1 

52 


MULTIPLICATION. 


5  times  1  horse  are  5  horses. 
5  times  2  cows  are  10  cows. 


5  times  3  pigs  are  15  pigs. 
5  times  4  sheep  are  20  sheep. 


Once  5 

2  times 

3  times 

4  times 

5  times 

6  times 

7  times 

8  times 

9  times 


LESSON    XL VIII. 

horses  are  5  horses. 
5  posts  are  10  posts. 
5  doors  are  15  doors. 
5  cows  are  20  cows. 
5  pigs  are  25  pigs. 
5  stys  are  30  stys. 
5  sheep  are  35  sheep. 
5  trees  are  40  trees. 
5  sheds  are  45  sheds. 


MULTIPLICATION. 

53 

I.X3SSON 

XLIX 

■ 

^^^ 

(See  Manual,  Sec.  I., 

Exercise  lY.) 

Copy,  complete,  aud  read  the  following 

tables : 

fix.  1. 

(1) 

(2) 

(3.) 

(4.) 

(«•) 

(6) 

II 

4x5 

6x5 

5x2 

5x5 

4x5 

2x5 

3x5 

2x5 

5x3 

3x5 

3x5 

3x5 

6x5 

3x5 

6x5 

6x5 

2x5 

4x5 

2x5 

7x5 

2x5 

4x5 

3x5 

3x5 

3x5 

2x4 

3x5 

3x5 

6x5 

6x5 

_4x5 

4x5 

2x5 

2x5 

3x5 

2x5 

fix.  2. 

a.) 

&■) 

(3.) 

(4.) 

(5.) 

(<5.) 

3x5 

6x5 

8x5 

9x5 

9x5 

3x5 

4x5 

7x5 

9x5 

7x5 

7x5 

5x5 

7x5 

3x5 

7x5 

8x5 

4x5 

9x5 

3x5 

0x5 

6x5 

5x5 

8x5 

7x5 

6x5 

7x5 

7x5 

7x5 

9x5 

6x5 

7x5 

6x5 

8x5 

8x5 

7x5 

3x5 

fix.  3. 

(1.) 

(2.) 

(3.) 

(4.) 

(«■) 

(6-) 

3  +  2 

7-5 

7+6 

7-5 

8  +  3 

5-0 

7x3 

6x5 

12-5 

8-5 

5  +  3 

5  +  0 

6  +  3 

6  +  5 

13-5 

7-5 

5  +  8 

0  +  5 

4-2 

14-5 

8+5 

13-5 

5-2 

0x5 

9-5 

13-5 

6  +  5 

5-3 

7+3 

5x5 

9x5 

12-5 

5-0 

5  +  3 

8-5 

7-5 

6« 

■^ 

I 

54 


MULTIPLICATION. 


LESSON    L. 

Once  6  sloops  are  6  sloops. 

2  times  6  steamboats  are  12  steamboats. 

3  times  6  towers  are  18  towers. 

4  times  6  houses  are  24  houses. 

5  times  6  men  are  30  men. 

6  times  6  birds  are  36  birds. 

7  times  6  men  are  42  men. 

8  times  6  masts  are  48  masts. 

9  times  6  flags  are  54  flap^s. 


Problems. — If  a  ship  have  3  masts,  how  many  masts  have  6  such 
ships  ?  Thore  are  12  sea-gulls  in  a  flock;  a  sailor  shot  5  of  them; 
how  many  escaped  ? 


MULTIPLICATION.  55 

y  i 

BSSON     LI.  I 

^.^-^        (See  Manual,  Sec.  I.,  Exercise  IV.) 

Copy,  complete,  and  read  the  following  tables: 

£x.  1. 


(!■) 

(2.) 

(3) 

(4.) 

(S-) 

(6.) 

5x6 

8x6 

7x6 

8x6 

5x6 

5x6 

4x6 

7x6 

9x6 

3x6 

3x6 

7x6 

3x6 

5x6 

5x6 

7x6 

9x6 

3x6 

4x6 

3x6 

8x6 

3x6 

3x6 

6x0 

3x6 

2x6 

9x6 

9x6 

8x6 

3x6 

2x6 

7x2 

3x6 

8x6 

9x5 

9x6 

EX»  2.        (1.)  .(2.)  (3.)  (4.)             (5.)  (6.) 

2  +  3  4x2  4  +  6  5+3  4  +  6  13-3 
6  +  4  3x6  <o-\-^  6  +  2  3  +  6  11-6 
4x6  5  +  6  4x6  4-3  6  +  3  12-6 

3  +  6  6-5  3  +  6  ^-(^  6-3  4  +  6 
6-3  13-6  8-6  ^-^^  5x6  12-6 
2  +  6  2x6  13—6  6x3  4  +  6  4x6 

Ex,  3.    (1.)  (2.)  (3.)  (4.)     (5.)  (6.) 

5  +  6  3  +  6  4+6  7x0  5  +  6  15-6 

5  +  3  6-3  4-2  6x0  ^y.^  13-6 

6  +  3  Y  +  4  4x6  6-0  6x5  10-6 
2  +  6  7x3  3x6  6  +  0  6-5  16-6 
6-2  7x6  7-6  0  +  6  7  +  6  11-6 
6-0  7+6  7-0  0x6  6+9  6+5 


LESSON   LII. 

Once  7  houses  are  7  houses.. 

2  times  7  windows  are  14  windows. 

3  times  7  doors  are  21  doors. 

4  times  7  carts  are  28  carts. 

5  times  7  men  are  35  men. 

6  times  7  women  are  42  women. 

7  times  7  trees  are  49  trees. 

8  times  7  churches  are  56  churches. 

9  times  7  dogs  are  63  dogs. 


Problems.— If  the  house  has  3  windows,  how  many  windows  will 
4  such  houses  have  ?  The  man  can  carry  7  bushels  of  apples  in  his 
cart,  how  many  bushels  can  he  carry  in  going  5  times  ?  The  woman 
went  to  market  7  times,  and  each  time  carried  7  eggs  in  her  basket ; 
how  many  eggs  did  she  carry  to  market?  There  are  13  large  stones 
by  the  side  of  the  road ;  if  6  of  them  should  be  carried  awav,  how 
many  would  remain  ?  On  a  rose-bush  there  are  5  roses ;  how"^  many 
roses  on  7  such  bushes  ? 


MULTIPLICATION. 

57 

LESSON 

I.III. 

(See  Manual,  Sec.  I., 

Exercise  IV.) 

Copy,  complete,  and  read  the  following 

tables : 

jBx.  1.      a.) 

(2.)     . 

(3) 

(■t) 

(5.) 

(6.) 

1             3x7 

4x7 

2x7 

5x7 

6x7 

5x7     i 

4x7 

6x7 

3x7 

0x7 

3x7 

6x7 

6x7 

3x7 

8x7 

5x7 

6x7 

4x7 

5x7 

8x7 

5x7 

8x7 

8x7 

6x7 

3x7 

6x7 

7x7 

8x7 

9x7 

3x7 

7x7 

5x7 

4x7 

6x7 

3x7 

5x7 

Ex.  2.       (1.) 

(2.) 

(3.) 

(4.) 

(5.) 

«5.) 

3x7^ 

-'■2x7 

5x7 

3x7  15-7 

6  +  7 

4x7  14-7 

6x7 

6x7 

8x7 

8x7 

12-7 

6x7 

8x7 

1  +  7 

6  +  7 

5  +  7     1 

3x7 

8x7 

9-7 

8-7 

9x7 

4x7     ! 

6  +  7  15-7 

6  +  7 

0x7 

6  +  7 

8x7 

_6  +  7 

4x7 

8x7 

6x7 

9x7 

9-7 

i  Ex.  3.        (1.) 

<2-) 

(S.) 

(4.) 

(5.) 

(6.) 

1             3x1 

3x3 

6  +  3  15-7 

8x5 

4+3     ' 

3  +  7 

4-3 

7-3 

7+8 

6x7 

7x7     : 

1             4x3 

8  +  6  16-7  16-8 

7x6 

7-7     1 

7-2 

4x3 

13-7 

4x3 

9-7 

3-3 

7+3 

5x7  16-7 

9  +  6 

8-6 

8-8 

6x7 

2-0 

10-7  16-7 

9  +  7 

4-4 

--» 

Once  8 

2  times 

3  times 

4  times 

5  times 

6  times 

7  times 

8  times 

9  times 


ponds  are  8  ponds. 
8  ducks  are  16  ducks. 
8  deer  are  24  deer. 
8  trees  are  32  trees. 
8  rocks  are  40  rocks. 
8  birds  are  48  birds. 
8  antlers  are  56  antlers. 
8  stones  are  64  stones. 
8  bushes  are  72  bushes. 


Problems.— Since  1  deer  has  4  feet,  how  many  feet  have  2  deer? 
Each  duck  has  two  wings  ;  how  manj  wings  have  2  ducks  ?  Each 
bird  has  2  wings;  how  many  wings  have  8  birds?  If  a  hunter 
should  hoot  3  of  the  birds,  how  many  would  escape? 


MULTIPLICATION.  59 


LESSON    LV. 

(See  Manual,  Sec  I.,  Exercise  IV.) 

Copy,  complete,  and  read  the  following  tables : 

Ex.  1.          (1.)             (2.)             (3.)             (4.)             (5)  (6.) 

3x8  4x8  4x8  4x8  5x8  5x8 

4x8  3x8  3x8  3x8  3x8  6x8 

3x8  7x8  6x8  6x8  7x8  7x8 

2x7  3x8  3x8  3x8  6x8  4x8 

5x8  6x8  7x8  7x8  3x8  3x8 

6x8  4x8  6x8  6xS    4x8  6x8 


Ex.  8,   (1.) 

(2.) 

(3.) 

(.*■) 

(«■) 

(6.) 

3x8 

2x8 

2x8 

4x8 

5x8 

3x8  : . 

7x8 

1x8 

4x8 

7x8 

6x8 

7x8 

2x8 

7x8 

7x8 

6x8 

7x8 

6x8  1 

3x8 

9x8 

6x8 

5x8 

6x8 

3x8  1 

7x8 

6x8 

3x8 

7x8 

7x8 

7x8  i 

3x8 

5x8 

1x8 

6x8 

5x8 

6x8   ; 

Ex,  3.    (1.) 

(a) 

(3.) 

<4.) 

(5.) 

(6.)     ! 

4+8  17-8 

5x7 

7-6 

7-4 

8-8  ' 

3  +  8  11-8 

7x8 

7+4  15-6 

8x0 

8-3 

3  +  9 

8-8 

5  +  9 

7x4 

0x8 

8-2 

6  +  7 

8x8 

9  +  5 

8  +  6 

8  +  0 

13-9 

4x7 

8  +  8 

9x8 

8x6 

0  +  8 

15-8 

7x3 

7x8 

7+8 

8-6 

8-0 

1 

60 


MULTIPLIOATIOif. 


LESSON   LVI. 

Once  9  horses  are  9  horses. 

2  times  9  hammers  are  18  hammers. 

3  times  9  anvils  are  27  anvils. 

4  times  9  tubs  are  36  tubs. 

5  times  9  cups  are  45  cups. 

6  times  9  barrels  are  54  barrels. 

7  times  9  boxes  are  63  boxes. 

8  times  9  whips  are  72  whips. 

9  times  9  men  are  81  men. 


Problems. — One  horse  has  4  feet,  how  many  feet  have  9  horses  ? 
A  man  can  shoe  5  horses  in  a  day,  how  many  horses  can  he  shoe  in 
8  days?  If  one  horse-shoe  requires  6  nails,  how  many  nails  should 
be  driven  in  2  horse-shoes?  In  4  horse-shoes?  There  are  3  horse- 
shoes hanging  on  one  side  of  the  door  and  3  on  the  other  side,  how 
many  on  both  ? 


MULTIPLICATION. 


61 


LESSON     LVII. 

(See  Manual,  Sec.  I.,  Exercise  IV.) 


Copy,  complete,  and  read  the  following 

tables : 

!i.  1.   (1.) 

(2.) 

(3.) 

(4.) 

(S.) 

(6.) 

3x9 

5x9 

3x9 

4x9 

3x9 

4x9  . 

4x9 

6x9 

6x9 

7x9 

7x9 

5x9  1 

3x9 

7x9 

3x9 

3x9 

6x9 

7x9 

7x9 

6x9 

7x9 

6x9 

3x9 

6x9 

6x9 

3x9 

3x9 

4x9 

8x9 

8x9 

5x9 

4x9 

0x9 

3x9 

3x9 

3x9 

X.  2.   (1.) 

(2.) 

(3.) 

(4.) 

(«.) 

! 

3x9 

3x3 

5x3 

4+3  15-7 

9-9 

4+6 

4-3 

7-3 

9-7  16-8 

9  +  0 

4x7 

4  +  6  18-9 

7x9 

10-9 

9x0 

3-2 

8-2 

13-7 

8x6 

7-3 

0  +  9  i 

7-2 

13-9 

15-6 

6-6 

7+3 

0x9  1 

9-8 

6-6 

9-8 

4+8 

4+3 

9-0 

x.  3.   (1.) 

(2.) 

(3.) 

(4-) 

'(«.) 

(6.) 

3x7 

3x7 

6x7 

4+7 

8  +  6 

8  +  3 

4x7 

8-4 

5x7 

8  +  6 

3  +  7 

7+3 

3  +  7 

7-7 

3  +  4 

8x7 

9  +  3 

8x7 

9x9 

8  +  3 

6  +  9 

9  +  7 

9x3 

9x7  j 

8  +  7 

7+7 

6-1 

9x7 

9-3 

6-4  i 

6x9 
«  ■ 

4x8 

8  +  7 

8  +  3 

4+6 

3  +  4 

LESSON   LVIII, 


How  many  times  can  2  tables  be  taken  from  2  tables  ? 
How  many  times  can  2  globes  be  taken  from  4  globes  ? 
How  many  times  are  2  maps  contained  in  6  maps  ? 
How  many  times  are  2  desks  contained  in  8  desks  ? 
How  many  times  are  2  boys  contained  in  10  boys  ? 
How  many  are  half  of  12  girls? 
How  many  are  on3  half  of  14  books  ? 
16  chairs  are  how  many  times  2  chairs  ? 
18  window-panes  are  how  many  times  2  window- 
panes  ? 


*  Note  for  the  Teacher.— The  teacher  should  not  fail  to  show  by  means 
of  objects,  tliat  2  can  be  taken  from  a  number  as  often  as  2  is  contained 
in  it,  or,  that  the  two  forms  of  expression  are  essentially  the  same. 


DIVISION.  63 


LESSON     lilX.* 

(See  Manual,  Sec.  L,  Exercise  V.) 

Copy,  complete,  and  read  the  following  tables : 

Ex.  1, 


Model. 

(1-) 

(2) 

(3.) 

(4.) 

4--2  =  2 

2-^2 

2^2 

2^2 

4-f-2 

8-T-2=4 

4--2 

8--2 

4--2 

16--2 

6-r-2  =  3 

8--2 

4-^2 

12^2 

14^2 

2^2=1 

10-^2 

12--2 

14^2 

12-T-2 

8h-2=4 

8--2 

10^2 

10^2 

16-^2 

2-f-2=l 

4^2 

6--2 

14-^2 

8-T-2 

Ex.  2.  Model.  (1.)  (2,)  (3.)  (4.) 

16-^2=8    12-^2    10^2    16-^-2  4^2 

18^2=9    16-^2      8-^2    12-f-2  8-^2 

12-^2=6    18-^2      6-^2    10^2  12^2 

10_^2=:5    20-^2      8^2      8-^2  14^2 

8^2=4    18-^2      4-^2    18-^2  4-^2 

6-f.2=3    16-f-2    16-^-2    12-^2  8-^2 

Ex.3.         (1.)  (2.)  (3.)  (4.)  (5.)  (6.) 

16~2     8-2     7-2     5-2  .5-2  4-2 

16-8     8-4-2  16-2     2-2     6-^2  6-^2 

8  +  8     8--2  14-^2     8  +  2     7  +  2  8-2 

7-6     8x2     6x2  10---2     2  +  8  18-f-2 

7+2     9-2     2+8     7-2     2x8  7-2 

12-9     6-2     9-2     4-f-2     8^2  12-2 

*  ^ote  for  the  Teacher.— innstrnte  the  meaning  and  the  use  of  the  sign 
of  Division  (-*-)  in  the  following  Exercises. 


3  carts  are  once  3  carts. 

6  horses  are  2  times  3  horses. 

9  boxes  are  3  times  3  boxes. 
12  pillars  are  4  times  3  pillars. 
15  windows  are  5  times  3  windows. 
18  men  are  6  times  3  men. 
21  doors  are  7  times  3  doors. 
24  canes  are  8  times  3  canes. 


Problems.— A  carman  had  27  boxes  to  take  to  the  depot,  how 
many  loads  will  they  make  if  he  draws  3  boxes  at  a  load'?  A  boy 
has  15  cents,  how  many  pencils  can  he  buy  if  they  cost  3  cents 
each  ?  A  lady  has  12  dollars,  and  if  silk  is  3  dollars  a  yard,  how 
many  yards  can  she  buy?  12  window-panes  are  how  many  times 
8  window-panes  ? 


DIVISION. 

65 

liBSSOM    LZI. 

(See  Manual,  Sec.  I.,  Exercise  V.) 

Copy,  read, 

and  complete  the  following 

tables : 

1 

Ex.  1.        (1.) 

(2.)           (3.)             (4.)            (6.) 

(«.) 

6^3 

6-^3  12^3  15-=-3  16^3 

15-=-3 

12^3 

9-^3  15^3  18^3  21^3 

21^3 

^       9-^3 

15-T-3  18H-3  15-^3  24-^3 

27--3 

■       3-h3 

12^3     6--3  21^3  18^3 

24^3 

■       9H-3 

9^3     9^3  18^3  15^3 

18^3 

"^       6-3 

12--3    3-^3    6^3  12^3 

15-=-3 

Ex.  a.      (1.) 

(2.)             (3.)             (4.)             (5.) 

(6.) 

27^3 

15-V-3  18^3  21--3  18--3 

12H-3 

24-- 3 

6^3  21^3  18^3  21^3 

9h-3 

15^3 

9-^3  24^3  24^3  27-=-3 

6H-3 

21^3 

12--3  27--3  27--3  18^3 

18-=-3 

27^3 

15^3  15^3  21-f-3  27-^3 

24-4-3 

24-=- 3 

18-^3  24^3  15-f-3  12-T-3  27^3 

Ex.  3.        (1  > 

(2.)             (3.)              (4.)            (5.) 

(6.) 

6-f-3 

4x3     8  +  3  12^3     6-=-3 

8x3 

4-3 

9x3     9+3     9x3    9^3 

3x3 

7+3  12^3  11-3     7-h3  11-3 

11-3 

8x3 

6+3     8x3     8-3     8x3 

24-^3 

24^3 

8—3  27^3     9-^3     9  +  3 

8  +  3 

7+3  11-3    7+3    8x3    7+3 

3  +  9 

i*-~ 

LESSON    LXII. 

4  birds  are  contained  in  4  birds  once. 
4  spokes  are  contained  in  8  spokes  2  times. 
4  bags  are  contained  in  12  bags  3  times. 
4  mills  are  contained  in  16  mills  4  times. 
4  posts  are  contained  in  20  posts  5  times. 
4  houses  are  contained  in  24  houses  6  times. 
4  windows  are  contained  in  28  windows  7  times. 
4  horses  are  contained  in  32  horses  8  times. 
4  men  are  contained  in  36  men  9  times. 


Problems.— One  wind-mill  has  4  wings,  how  many  wings  will  4 
such  mills  have?  How  many  loads  will  16  bags  of  corn  make  if  a 
man  draws  4  bags  at  a  load  ?  There  are  4  windows  in  the  house, 
how  many  windows  will  6  such  houses  have  ?  There  are  8  spokes 
in  a  wheel ;  how  many  spokes  in  2  wheels  ?  If  a  cart  have  2  wheels, 
how  many  wheels  have  4  carts  ?  i 


DIVISION. 

67 

LESSON 

LXIII 

. 

(See  Manual,  Sec.  I. 

,  Exercise  V.) 

Copy,  complete,  and  read  the  following 

1 
tables : 

BX.  1.       (1.)              (2.)            (3.) 

(*•) 

(5.) 

(C.) 

4^4     4-T-4     8^4 

24^4 

28-^4 

32^4 

8  :  4  12  :  4  12  :  4 

16^4 

32-^4 

20^4 

12H-4  16^4  16-h4  12-^4 

28--4  28^4 

8^4  12--4  20-^4 

8^4 

24^4 

24^4 

12-^4    8-^4  12H-4 

36^4 

16-h4 

32^4 

4-^4  16-^4    8^4  20^4 

124-4 

28H-4 

1 

Ex.  8.         (1.)           (2.)           (3.) 

(4.) 

(«•) 

j 
(6.) 

32^4    4-T-4    8^4 

4-V-4 

28-^4 

12-^4 

24^4    8--4  12H-4 

8^4 

20-H-4 

20^4     ■ 

12---4  24^4  32-^4 

16^4 

16^4 

28-^4 

8^4  36H-4  36^4 

24:  4 

20-=-4 

32-T-4 

20^4  28--4  24^4 

28---4 

28^4 

8-^4 

16^-4  20-^4  12-^4 

36-^4 

36-^4 

4--4 

Ex.3.         (1.)            (2.)            (3.) 

(4.) 

(5.) 

(6.)            1 

24^4  32^4    6x4 

8-4 

5x4 

4x8     ' 

8x4    8x4    7—4 

7x4 

7-4 

9+4 

12-4    6-4    8x4 

36-=-4 

8x4 

9-4 

6+4    8+4    7+4 

7-4 

4x8 

32^4 

8-^4  13-4  13-4 

12-4 

9x4 

7x4 

7+4    7x4    7x4 

6  +  4  36^4 

6-4 

68 


DIVISION. 


LESSON   LXIV. 

5  barrels  are  once  5  barrels. 
10  men  are  2  times  5  men. 
15  boxes  are  3  times  5  boxes. 
20  boats  are  4  times  5  boats. 
25  logs  are  5  times  5  logs. 
30  baskets  are  6  times  5  baskets. 
35  sea-gnlls  are  7  times  5  sea-gulls. 
40  rods  are  8  times  5  rods. 
45  lines  are  9  times  5  lines. 


Problems. — There  were  17  piles  lying  on  the  dock  ;  9  have  been 
driven ;  how  many  remain  ? 


DIVISION. 

69 

LSSSON    LXV. 

(See  Manual,  Sec.  I.,  Exercise  V.) 

Copy,  read,  and  complete  the  following  tables : 

Ex.  1.        (1.)            (2.) 

(3.)             (4.) 

(S.)             (6.) 

5-5  25^5 

30-^5  15-^5 

40^5  40^6 

15-f-5  15-H-5 

25--5  30^5 

15--5  30--5 

10^5     5^5 

20-^5  35^5 

25^5  45^5 

20-^5  10--5 

15^5  40^5 

35^5  15^5 

10^5  20-^5 

10^5  35-^5 

20-^5  25-f-5 

5^5  25^5 

15-^5  15^5 

40-:-5  20^5 

Ex.  a.     (1.)       (2.) 

(3.)             (4.) 

(«.)            (6.) 

25-^5  15-^6 

20^-5     5-V-5 

IOh-5  15-=-5 

30^5  lO-r-5 

35-^5  15-^5 

20-^5  25^5 

40^5     5^5 

40^5  25^5 

30-=-5  30-^5 

20^6  30-f-5 

25^5  35^5 

40^5  40^5 

45^5  40-^5 

30^5  45-^5 

15-T-5  45^5 

10-^5  45-^5 

20^5  25-^5 

20-^5  35-^5 

Ex.  3.        (1.)             (2.) 

(3.)              (4.) 

(5.)             (6.) 

25^5  30^5 

7+5  45--5 

6+5    4x5 

4x5     7x5 

8+5     7x5 

12-6  11-5 

!             3+5     5-5 

13-5     5x5 

8  +  7  10^5 

8-5     8  +  5  40-=-5  10-5 

8—5     3x5 

14-5     5x8 

6x6  10^5 

8x5     7+5 

10^5  13-5 

7-5  10x5 

6+5     9+6 

i 

70 


DIVISION. 


LESSON   LXVI. 

6  cliiirches  are  once  6  churches. 
12  sheep  are  2  times  6  sheep. 
18  ducks  are  3  times  6  ducks. 
24  dogs  are  4  times  0  dogs. 
30  men  are  5  times  6  men. 
36  boys  are  6  times  6  boys. 
42  saddles  are  7  times  6  saddles. 
48  bridles  are  8  times  6  bridles. 
54  horses  are  9  times  6  horses. 


Problkms. — Willie  rode  2  hours  every  day  for  a  week,  how 
many  hours  did  he  ride  in  all  ? 


Divisiojsr.                              71 

1 

LESSON    LXVII. 

i 
j 

(See  Manual,  See  I.,  Exercise  V.) 

Copy,  complete,  and  read  the  following  tables :   ' 

Ex.  1 

(1.)            (2.)           (3.)            (4.)            (5)            (6,)           1 

G-:-6  30-r-6  30-^6  42^6  48^6  54-=-6     ; 

18-^6  18-T-6  30^6  12^6  30^6  48-^6     ' 

12^6     6-^6  24^6    Q^Q  36-=-6  36-r-6     | 

IK 

24-4-6  18-^6  18^6  30-^6  48--6  42^6 

6-4-6  30-4-6  12^6  42-^6  24-4-6  24-^6 

1 

18^6  24-4-6     6^0  18^6  18-4-6  54-^6 

Ex.  2 

.        (1.)             (2.)              (3.)             <4.)             (5.)             (6.) 

42-4-6  12-4-6  24-4-6  30-4-6  42^6  18^6 

48-^6  18^6  30^6  36^6  30^-6  24^6 

30^6  30-=-6  42^6  42^6  36-4-6  36^6     | 

12^6  42^6  48^6  54-4-6  48^6  48-=-6 

54^6  54^6  18^6     6-4-6  18^6  42^6 

! 

30-4-6  18^6  12-^6  18-=-6  12-4-6  54^6 

£x.  3 

(1.)             (2.)             (3.)             (4.)            (5.)             (6.) 

24-4-6     6x8    7-6     5x6    4x6  13-6 

24^4    5x6     5x6    7-5     8x8    7-6 

IKv 

2x6  13-6  13-6  13-6     7-6     8x6 

p 

15-6     7-f6  15-6     7x6     7x6    4-1-6 

13-6     8-f6     8-f6  12^6  14-6     8x6 

8x6  48-4-6     8x6     8-6  11-6    7x6 

" 

DIVISION. 


LESSON   LXYin. 

7  baskets  are  once  7  baskets. 
14  hop-poles  are  2  times  7  bop-poles. 
21  men  are  3  times  7  men. 
28  girls  are  4  times  7  girls. 
35  hop-vines  are  5  times  7  hop-vines. 
42  birds  are  6  times  7  birds. 
49  hats  are  7  times  7  hats. 
56  coats  are  8  times  7  coats. 
63  knives  are  9  times  7  knives. 


Problems.— There  are  8  birds  flying  away  from  the  hop-yard  ; 
they  are  separated  into  2  flocks;  how  many  birds  in  each  flock  ? 


1 

DIVISION.                                             73 

LESSON    LXIX. 

(See  Manual,  Sec  I.,  Exercise  V.)                                 ! 

Copy,  complete,  and  read  the  following  tables : 

Ex.1.        (1.)               (2)             (3.)              (4.)             (5.)            (6.) 

7-^7  28^7  42-^7  49-^7  49^7  63-r-7 

14-^7  21-^7  14-^7  42^7  56^7  28-=-7     ; 

284-7  35^7  21-V-7  28-^7  42^7  14^7 

21H-7  21^7  35-^7  49h-7  63^7  42-=-7  ' 

14--7  14--7  42--7  14-v-7  56-^7  21--7 

28-^7    7-4-7  14-^7    7-^7  28-=-7  56^7 

i 

Ex.  2.           (1.)              (2.)              (3.)              (4.)              (5.)              (6.) 

49-^7  21^7  21-^7  28-^7  28-=-7  14-=-7 

42^7  14^7    7-^7  14---7    7^7  21-j-7 

35--7  35--7  28--7  42--7  21--7  35-^7     | 

28^7  49^7  35-^-7  49-^7  35^7  49^7 

56-^7  63-f-7  56-^7  63-=-7  49-^7  63-f-7 

21-^7  42--7  G3-^7  35h-7  63^7  56--7 

Ex.3.          (1.)               (2.)              (3.)              (4.)              (5.)              (6.) 

49-^7  21-^7    8-t-7    .5x7    4x7    4x7 

Cx7  35-r-7    5-F7    8x7    G  +  7    C-l-7 

8x7  16-7    9-7  28^7    9-h7    9-h7 

15-7    4x7    6x7  66-^7    9-7    8-7 

6-F7    5x7    5x7    8x7    8x7    7x7 

5-1-7    6-r7  63-h7    6x7  43--7  28-f-7 

T 

74 


DIVISION. 


LESSON   LXX. 

8  cows  are  once  8  cows. 
16  hens  are  2  times  8  hens. 
24  houses  are  3  times  8  houses. 
32  feet  are  4  times  8  feet. 
40  claws  are  5  times  8  claws. 
48  dishes  are  6  times  8  dishes. 
56  boards  are  7  times  8  boards. 
64  doors  are  8  times  8  doors. 
72  windows  are  9  times  8  windows. 


Problems.— Henry  found  a  nest  containing  8  eggs;  how  many 
eggs  will  2  such  nests  contain  ?  The  cow  gives  8  quarts  of  milk 
every  night  and  morning ;  how  many  quarts  does  she  give  each 
day? 


DIVISION. 


75 


LBSSON    liZZI. 

See  Manual,  Sec.  I.,  Exercise  V.) 


Copy,  complete,  and  read  the  following  tables : 


Ex.  1. 


(1.)             (2.)            (3.)            (4.)             (5.)             <6.) 

32- 

-8  40- 

-8  56- 

-8  24- 

-8  48- 

-8  73-- 

16- 

-8     8- 

-8  40- 

-8  32- 

-8  64- 

-8  32^ 

8- 

-8  24- 

-8  32- 

-8  56- 

-8  48- 

-8  64^ 

32- 

-8  32- 

-8  16- 

-8  48- 

-8  64- 

-8  48^ 

24- 

-8  40- 

-8  24- 

-8  40- 

-8  56- 

-8  64-f- 

16- 

^8  24- 

-8  48- 

^8  56- 

-8  40- 

-8  40^ 

£x.  2. 


(1.)           (2.)             (3.)             (4.)             (5.)            (6.) 

40- 

-8  48- 

-8  56- 

-8  24- 

-8  24- 

-8  48-; 

48- 

-8  56- 

-8  72- 

-8     8- 

-8  56- 

-8  56-^ 

72- 

-8  72- 

-8  56- 

-8  48- 

-8  40- 

-8  72^ 

32- 

-8  24- 

-8  40- 

-8  16- 

-8  48- 

-8  24h 

48- 

-8  64- 

-8  48- 

-8  64- 

-8  32- 

-8     8-; 

32- 

-8  40- 

^8  64- 

-8  24- 

-8  24- 

-8  72-= 

Ex.  3.         (1.)               (2.)  (3.)              (4.)             (5.)  (6.) 

40_^8  32-^8  72-f-8  40-f-8  15-8  48-^8 

6x8  4x8  64-^8  6x8  48-f-8  6  +  8 

7  +  8  6x8  7x8  72^8  6x8  16-8 

16-8  8x8  3x8  9-8  15-8  11-8 

17_8  13-8  15-8  7  +  8  94-8  3x8 

14-8  5  +  8  12-8  6x8  6  +  8  8x7 


LESSON   LXXIl. 

9  men  are  once  9  men. 
18  boats  are  2  times  9  boats. 
27  poles  are  3  times  9  poles, 
36  brido;es  are  4  times  9  bridges. 
45  trees  are  5  times  9  trees. 
54  rocks  are  6  times  9  rocks. 
63  birds  are  7  times  9  birds. 
72  fishes  are  8  times  9  fishes. 
81  fish-lines  are  9  times  9  fish-lines. 


Pkoblems.— A  man  caught  4  fishes  the  first  hour  and  7  the  next 
hour,  how  many  did  he  catch  in  the  2  hours  ? 


DIVISION.  77 


LESSON     liXXIII. 

(See  Manual,  Sec  I.,  Exercise  V.) 

Copy,  complete,  and  read  the  following  tables : 

fix.  1.         (1.)  (2.)  (3.)  (4.)  (5)  (6.) 

9-f-9  45-^9  45-^9  63^9  72-^9  36-^9 
18-^9  27-^9  54-r-9  27-f-9  63-9  63^9 
36-T-9  45-^9  36^9  18-^9  54-^9  54^9 
27-^9  36-^9  18-f-9  63-^-9  45-^-9  72-^9 
18-^9  45-9  9-^9  54^9  72^9  81-^9 
27-^9  36---9  27-^9  63^9  27-^9  63-f-9 

Ex.  2.        (1 )  (2.)  (3.)  (4.)  (5.)  (6.) 

54_^9  45^9  27-f-9  18-^9  45-^9  18^9 
63^9  54-T-9  36-f-9  27-^9  63-v-9  9-^9 
81-^9  63-^9  634-9  9-^9  81^9  27-^9 
18-^9  81-^9  81-^9  45-^-9  72-^9  63-^9 
45-^9  36-T-9  63-^9  27-r-9  81h-9  36-^9 
27-^9  63-T-9  54-^9  81-h9  18-^9  45-^9 

Ex.  3.         (1.)  (2.)  (3.)  (4.)  (5.)  (6.) 

6x8  5x9  6  +  9  9  +  1  45--9  63-^9 

81-^9  72-f-9  17-9  9x9  5x9  4x9 

8x9  63-f-9  36-^9  27-^9  45^9  9  +  9 

3  +  9  18-9  8x9  10-9  5  +  8  9~9 

9  +  6  9x9  6  +  9  1  +  9  13-9  8x9 

17-9  7x7  17-9  10  +  8  8x8  18-^9 

7* 


78 


FRACTIONS. 


FEACTIONS. 


LESSON     LXXIV. 

(See  Manual,  Sec.  I.,  Exercise  VI.) 


Two  halves. 


Three  thirds. 


Four  fourths. 


Five  fifths. 


How  many  halves  in  one  apple  ? 
How  many  halves  in  one  peach  ? 
How  many  thirds  in  one  pie  ? 
How  many  thirds  in  one  fish  ? 
How  many  fourths  in  one  horse? 
How  many  fourths  in  one  loaf? 
How  many  fifths  in  one  string  ? 
How  many  fifths  in  one  stick  ? 


One  half.  One  third.  Two  fourths.  Three  fifths. 

How  many  halves  make  one  melon  ? 
How  many  thirds  make  one  pear  ? 
How  many  fourths  make  one  orange  ? 
How  many  fifths  make  one  apple  ? 


UNITED   STATES  MINT. 
money. 

A  mint  is  the  place  where  money  is  made. 

Federal    JTIoney. 

Federal  money  is  the  currency  of  the  United  States. 

LESSON    LXXV. 
(See  Manual,  Sec.  I.,  Exercise  VII.) 

10  mills  (m.)  make  1  cent.  ct. 

10  cents  make  1  dime.  d. 

10  dimes         make  1  dollar.  $. 

10  dollars       make  1  ea^le.  E. 


80 


FEDERAL    MONEY. 


American  Coins. 


Copper, 


Silver. 


Silver. 


ENGLISH    MONEY. 


81  i 


LESSON    LXXVI. 

(See  Manual,  Sec.  I.,  Exercise  VII) 

English  Money. 

English  money  is  the  currency  of  Great  Britain. 

TABLE. 

4  farthings  (far.)  make     1  penny.  d. 

12  pence  make     1  shilling.  s. 

20  shillings  make  ]  ^  P«™^  «/      I  £. 

^  I        sovereign,  j 


Far.— Copper -5  mills.         Sov.— Gold— $4  84.  Silver— 18  cents. 

JV^oie. — The  franc  is  a  French  coin. 


82 


ENGLISH    MONEY. 


Avoirdupois  Weight. 

Avoirdupois  weight  is  used  for  weighing  all 
common  articles. 

LESSON    LXXVn. 


(See  Manual,  Sec.  I.,  Exercise  VII.) 


16  drams  (dr.)  make  1 

16  ounces  make  1 

25  pounds  make  1 

100  pounds  or  )  ^^^^ 
4  quarters      ) 
20  hundred  weight  make  1  ton. 


ounce, 
pound, 
quarter, 
hundred 
weight 


oz. 
lb. 
qr. 


i  ^''''^Z^  \  cwt. 
(   weight   ) 


AVOIRDUPOIS   WEIGHT. 


83 


LESSON    LXXVIII. 
Avoirdupois  'Weigbt  -  Continued. 


437i  gr. 


7000  gr. 


*  jifote. — ^The   exact  weight  of  an  Avoirdupois  dram  is  I^W 
Troy  grains. 


8i 


TROY    WEIGHT. 


Troy  \¥eiglit, 

Troy  weight  is  used  in  weighing  gold;  silver, 
and  jewels,  and  in  philosophical  experiments. 

LESSON    LXXIX. 
(See  Maimal,  Sec.  I.,  Exercise  VII.) 

24  grains     (gr.)     make  1  pennyweight,  pwt. 
20  pennyweights  make  1  ounce.  oz. 

12  ounces  make  1  pound.  lb. 

3*2  grains  make  1  carat.  k. 


24  grs.  480  grs.  576( 

Note.Sl  grains  make  a  carat,  Diamond  weight 


5760  grs. 


apothecaries'    WEIGfHT. 


85 


Apothecaries'  Weiglit. 

LESSON   LXXX. 

(See  Manual,  Sec.  I,  Exercise  VII.) 

20  grains  (gi\)  make  1  scruple,  sc.  or  3. 

3  scruples       make  1  dram.     dr.  or  3 . 

8  drams  make  1  ounce,    oz.  or  §. 

12  ounces         make  1  pound,    lb.  or  ft>. 


^® 


20  grs.  60  grs. 


480  grs. 


6760. 


liong  Measure* 

Teacher. — Arthur,  can  you  tell  me  how  far  a  wile  is? 

Arthur. — If  I  place  12  sticks  an  inch  long  in  a  row, 
the  row  will  be  Sifoot  long. 

If  I  make  a  measure  8  times  as  long  as  the  row  of 
sticks,  it  will  be  a  yard  measure,  like  the  one  on  the 
table. 

Five  and  a  half  times  the  yard  measure  will  be  a  rod, 
and  is  just  the  width  of  the  room. 

Forty  times  the  width  of  tbe  room  is  the  distance 
between  every  other  telegraph  pole,  or  one  furlong. 

Eight  times  the  distance  between  every  other  tele- 
graph pole  is  the  distance  t  o  the  railroad-bridge,  or  one 
mile» 


LONG   MEASURE.  871 


LESSON     LXXXI. 

(See  Manual,  Sec.  I.,  Exercise  VII.) 
Long  Measure. 

Long  measure  is  used  for  measuring  distance. 

TABLE. 

12  inches  (in.)    make  1     foot.  ft. 

3  feet  make  1     yard.  yd. 

?t  ri"?     A    \  «iake  1  \  ^°^'  P^f  ^'  I  rd. 
11  halt  yards  )  (     or  pole.     ) 

40  rods  make  1     furlong.  fur. 

8  furlongs         make  1     mile.  mi. 

69i  statute  miles  |       .     .   .  -, 

277  quarter  miles  f  "^^^^  ^  ^^S'^^*  ^^S- 

360  degrees  make  1  circle  of  the  earth,   cir. 

Gniiter's  Cbain  Measure* 

Gunter's  Chain  Measure  is  used  by  surveyors. 

TABLE. 

25  links  (li.)  make     1     rod.  rd. 

4  rods  or    1        T        -,       1    .  -, 

100  links        \  ""^^'^     ^     ^^^^^°-  .       ^^- 

80  chains        make     1     mile.  mi. 


iiM  I  I 


1  Inch. 
Note. — A  link  is  about  11  inches  in  length. 


SQUARE   MEASURE, 


Square   Measure. 

Father. — Charley,  if  yon  wish  to  know  the  size  of  an 
acre,  cut  144  pieces  of  pnper  one  inch  square,  and  place 
them  on  the  tahle;  this  is  cnlled  a  square /(?o^. 

To  make  a  square  yard^  place  9  single  squares  in  a 
square,  which  is  just  the  size  of  the  table. 

To  make  a  piece  of  land  the  size  of  the  grass-plat  in 
the  door-yard,  it  will  require  30^^  square  yards,  which  is 
called  a  square  rod. 

Forty  square  rods  is  just  one  rood^  or  a  quarter  of  an 
acre  of  land,  and  is  the  size  of  the  lot  across  the  road  in 
which  you  see  the  sheep. 

Four  such  lots  contain  4  roods  of  land,  and  is  called  an 
acre. 


SQUARE   MEASURE.  89 


LESSON    LXXXII. 

(See  Manual,  Sec.  I.,  Exercise  VII.) 
Square  Measure. 

Square  measure  is  used  in  computing  the  area 
of  surfaces. 

TABLE. 

144     square  inches  (in.)  make  1  square  foot. 

9     square  feet  make  1  square  yard. 

SOi  square  yards  or  )    ^^^^  ^  ^  ^^^ 

121     qr.  square  yards  )  ^ 

.r.  1  1     -I  (  rood  or  quarter 

40     square  rods  make  1  j      ^^  ^,^  \^^^^ 

4  I  "^""^^^l^  ^""'^^  ^'^  I  make  1     acre. 

^.n  1     -I  (  square  mile  or 

640     acres  make  1  ^    ^         , . 

(         section. 

SurTeyorjs'  Square  Measure. 

Surveyors'  square  measure  is  used  in  comput- 
ing the  area  or  contents  of  portions  of  land. 

TABLE. 

625  square  links     make  1  square  rod.  sq.  rd. 

16  square  rods      make  1  square  chain,  sq.  ch. 

10  square  chains  make  1  acre.  A. 

640  acres  make  1  square  mile.  sq.  mi. 

36  square  miles    make  1  township.  T. 


CUBIC    MEASURE, 


Cubic  Measnrc. 

In  building  the  walls  of  a  cellar,  or  of  a 
building,  the  amount  of  stone  or  brick  used  is 
determined  by  cubic  measure.  A  cubic  inch  is 
a  square  block  1  inch  long,  1  inch  wide,  and  1 
inch  thick,  thus : 


tl"l  'l  'I  'I  'I  I  '!  'l  -\  'I 

A   row  of  10  cuLk  inches. 


A  tier  of  100  cubic  inchcB. 


CUBIC   MEASURE. 


91 


LESSON    LXXXIII. 

(See  Manual,  Sec.  I.,  Exercise  VII.) 
Cubic  Measure, 

Cubic  measure  is  used  to  estimate  the  con- 
tents of  solids. 

TABLE. 


1728 
27 
40 

50 

16 

8 

128 


cubic  inches 

cubic  feet 

cubic  ft.  of  round 

timber  or 

cubic  ft.  of  hewn 

timber 

cubic  feet 

cord  feet  or  ) 
cubic  feet       ( 


24|  cubic  feet 


make  1  cubic  foot, 
make  1  cubic  yard. 

-  make  1  ton  or  load. 

make  1  cord  foot. 

make  1  cord  of  wood. 

(  perch  of 

make  1  •<  stone  or 

f  masonry. 


Cubic  inch. 


Cubic  foot. 


Cubic  yard. 


92 


WmE   MEASURE. 


"Wine  Measure. 

Wine  measure  is  used  in  raeasuring  liquids. 


LESSON    XXXIX. 

4     gills  make  1  pint. 

2     pints  make  1  quart. 

4     quarts  make  1  gallon. 

63*  s>r  I  -*=  1  "'■""• 

2    barrels  or 
63 


pt. 

qt. 

gal. 

bbl. 


ZD  1 

ffaUoir''   \  make  1  hogshead,    hhd. 


^1^^      ,^^^- 


DEY    MEASURE. 


93 


Dry  treasure. 

Dry  measure  is  used  in  measuring  vegetables 
and  articles  not  fluid. 

LESSON   LXXXV. 
(See  Manual,  Sec.  I.,  Exercise  VII.) 

2  pints  (pt.)  make  1  quart.  qt. 

8  quarts         make  1  peck.  pk. 

4  pecks  make  1  bushel.         bu. 


! 


94 


MEASURE   OF   TIME. 


Ifleasure  of   Time. 

Time  is  the  measure  of  duration. 

LESSON   LXXXVI. 

(See  Manual,  Sec.  I.,  Exercise  V.) 

60  seconds  (sec.)  make  1  minute. 

60  minutes  make  1  hour. 

24  hours  make  1  day. 

7  days  make  1  week. 

4  weeks  and  2  days  or  )       i  ,i 

30  days  J  make  one  month. 

365  days  make  a  year.        yr, 

52  weeks  make  a  year.        yr. 

12  calendar  months  make  a  year.       yr. 


mm. 
h. 
da. 
wk. 

mo. 


■^ 


CIKCULA.R   AND   AITGULAE   MEASURES.  95 

LESSON     LXXXVII. 

(See  Manual,  Sec.  I.,  Exercise  VI.) 
Circular  Measure. 

Circular  measure  is  used  in  measuring  arcs  of 
circles. 

TABLE. 

60  seconds    ('')  make  1  minute.                  ' 

60  minutes  "      1  degree.                  ° 

90  degrees  "      1  quadrant.          qad. 

4  quadrants  "      1  circumference,  cir. 


Angular  ITIeasnre. 

Angular  measure  is  used  for  measuring  differ- 
ence of  directions. 

TABLE. 

60  seconds  (")  make  1  minute. 

60  minutes  "      1  degree.  ° 

90  degrees  "      1  right  angle,     r.  a. 


96 


MISCELLANEOUS   TABLES. 


Season. 

Winter, 


LESSON    LXXXVIII. 
Miscellaneous  Tables. 

DIVISION    OF    THE   TEAR. 


Names  of  months. 

1.  January, 

2.  February, 

3.  March, 

4.  April, 

5.  May, 

6.  June, 

7.  July, 

8.  August, 

9.  September, 

10.  October, 

11.  November, 

12.  December, 


No.  of  days. 

31 

28  or  29 

31 
30 
31 

30 
31 
31 

30 
31 
30 

31 

365  or  366 


Abbreviations. 

Jan. 
Feb. 

Mar. 
Apr. 

Jun. 

^  Aug. 

Sept. 
Oct. 

Nov. 

Dec. 


COUNTING. 

12  units  or  things  make  1  dozen. 
12  dozen  "      1  gross. 

12  gross  "      1  great  gross. 

20  units  "      1  score. 


PAPER. 

24  sheets  make  1  quire. 


20  quires 
2  reams 
5  bundles 


"      1  ream. 
"     1  bundle. 
"     1  bale. 


SEASONS. 


{March,  (  June, 

April,  Summer  <  July, 

May.  I  August. 

I  September,  i  December, 

October,  Winters  January, 

November.  (  February, 


Thirty  days  hath  September,     I     February  hath  twenty-eight,* 
April,  June,  and  November,        |     And  thirty-one  the  others  rate. 

*  Every  leap-year,  February  has  twenty-nine  days. 


98 


BOM  AN   NOTATION. 


LESSON    LXXXIX. 
Table  of  Roman   Notation. 


I     denotes 

II 

III 

IV  " 

y 

YI 

VII 

VIII      " 

IX 

X 

XI 

XII 

XIII  " 

XIV  " 
XV 

XVI  « 

XVII  " 

XVIII  " 

XIX  " 
XX 

XXI  " 

XXII  " 
XXII  " 
XXIV  « 


one. 

two. 

three. 

four. 

five. 

seven, 

eight, 

nine. 

ten. 

eleven. 

twelve. 

thi/teeh. 

fourteen. 

fifteen. 

sixteen. 

seventeen. 

eighteen. 

nineteen. 

twenty. 

twenty-one. 

twenty-two. 

twenty-three. 

twenty-four. 


XXX  denotes  thirty.         ; 

XL  "  forty.  I 

L  "  fifty.  ! 

LX  "  sixty. 

LXX  "  seventy.  ; 

LXXX  "eighty.  | 

XC  "ninety. 

C  "  one  hundred.     1 

CC  "  two  hundred. 

CCC  "  three  hundred. 

CCCC  "  four  hundred. 

D  "  five  hundred. 

DC  "  six  hundred. 

DCC  "  seven  hundred. 

DCCC  "  eight  hundred. 
DCCCC  "  nine  hundred. 

M  "  one  thousand. 

MD  "fifteen  hundred 

MM  "  two  thousand. 

X  "  ten  thousand. 

XI  "  eleven  th'sand. 
M  "  one  million.  ; 
MM  "  two  millions,    j 


FINIS. 


5      'ff 


sai^^ 


